MATH-1300-HBL2

Course administration

• Canvas page (TBA).
• Help with DjVu (if you have trouble reading the DjVu files on this page).
• SCC syllabus (DjVu).
• SCC Course Statements.
• SCC Student Technical Support Resources (DjVu).
• My course policies (DjVu TBA).
• Class hours: Tuesdays and Thursdays from 9:30 to 10:50 in room T5.
• Final exam time: May 5 Tuesday from 9:30 to 11:10 in room T5 (or by appointment).

Contact information

• Name: Toby Bartels, PhD.
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Office hours: Tuesdays and Thursdays from 1:10 PM to 3:15 (or by appointment) in room U9C (or over Zoom meeting 610-024-2876).

Readings

All of the dates below (and most of the numbering) are wrong.

Try to read this introduction before the first day of class:

• Objectives:
  • Understand what to expect from this course;
  • Know how to submit assignments.
• Reading:
  • My course policies (DjVu TBA, same as above);
  • My online introduction.
• Exercises from the textbook due on August 19 Tuesday or ASAP thereafter (submit these through MyLab): O.1.1, O.1.2, O.1.3, O.1.4, O.1.5, O.1.6, O.1.7, O.1.8, O.1.10, O.1.11, O.1.12.

Graphs and functions

1. General review:
   • Reading: Skim Appendix A (except Section A.4) from the textbook, and review anything that you're shaky on.
   • Exercises due on August 20 Tuesday (submit these on Canvas or in class):
     1. Which of the following are equations? (Say Yes or No for each.)
        1. 2x + y;
        2. 2x + y = 0;
        3. z = 2x + y.
     2. You probably don't know how to solve the equation x⁵ + 2x = 1, but show what numerical calculation you make to check whether x = 2 is a solution.
     3. Write the set {x | x < 3} in interval notation and draw a graph of the set.
     4. Suppose that ax² + bx + c = 0 but a ≠ 0; write down a formula for x.
   • Exercises from the textbook due on August 21 Wednesday (submit these through MyLab): A.6.25, A.6.43, A.6.75, A.6.99, A.7.63, A.9.71, A.9.75, A.8.33, A.8.47.
2. Graphing review:
   • Reading:
     • Review Section 1.1 through "Rectangular Coordinates" (pages 2&3) from the textbook;
     • Read Section 1.2 (pages 9–17) from the textbook (this should be review at the start but might be new material by the end);
     • My online notes on symmetry and intercepts.
   • Exercises due on August 21 Wednesday (submit these on Canvas or in class):
     1. Fill in the blanks with vocabulary words: The two number lines that mark the coordinates in a rectangular coordinate system are the coordinate _____, and the point where they intersect is the _____.
     2. Fill in the blanks with a vocabulary word: Given a graph in a coordinate plane, a point on the graph that lies on at least one coordinate axis is a(n) _____ of that graph.
     3. Fill in the blank: If for each point (x, y) on a graph, the point (−x, y) is also on the graph, then the graph is symmetric with respect to the _____.
   • Exercises from the textbook due on August 22 Thursday (submit these through MyLab): 1.1.15, 1.1.17, 1.2.13, 1.2.17, 1.2.23, 1.2.29, 1.2.31, 1.2.33, 1.2.35, 1.2.41, 1.2.43, 1.2.45, 1.2.47, 1.2.53, 1.2.55, 1.2.61, 1.2.67, 1.2.71, 1.2.77.
3. Graphing lines:
   • Reading:
     • The rest of Section 1.1 (pages 3–6) from the textbook;
     • My online notes on lines and line segments;
     • Section 1.3 (pages 21–31) from the textbook.
   • Exercises due on August 22 Thursday (submit these on Canvas or in class):
     1. Fill in the blanks with algebraic expressions: The distance between the points (x₁, y₁) and (x₂, y₂) is _____, and the midpoint between them is (___, ___).
     2. Write an equation for the line in the (x, y)-plane with slope m and y-intercept (0, b).
     3. Fill in the blanks with words or numbers: The slope of a vertical line is _____, and the slope of a horizontal line is _____.
     4. Fill in the blanks with numbers: Suppose that a line L has slope 2. The slope of any line parallel to L is ___, and the slope of any line perpendicular to L is ___.
   • Exercises from the textbook due on August 23 Friday (submit these through MyLab): 1.1.19, 1.1.33, 1.1.39, 1.1.47, 1.3.2, 1.3.7, 1.3.8, 1.3.13, 1.3.15, 1.3.17, 1.3.19, 1.3.21, 1.3.23, 1.3.25, 1.3.27, 1.3.29, 1.3.31, 1.3.45, 1.3.51, 1.3.53, 1.3.57, 1.3.63, 1.3.67, 1.3.73, 1.3.75, 1.3.79, 1.3.85, 1.3.91, 1.3.93, 1.3.111, 1.3.113.
4. Systems of equations:
   • Reading:
     • Section 11.1 (pages 720–730) from the textbook;
     • My online notes and video on systems of equations.
   • Exercises due on August 23 Friday (submit these on Canvas or in class):
     1. Answer Yes or No: Suppose that you have a system of equations and a point that might be a solution. If the point is a solution to one equation in the system but not a solution to another equation in the system, then is that point a solution to the system of equations?
     2. Given a system of two equations in the two variables x and y, if the graphs of the two equations intersect at (and only at) the point (3, 5), then what is the solution of the system? (Give explicitly the value of x and the value of y.)
     3. Consider the system of equations consisting of x + 3y = 4 (equation 1) and 2x + 3y = 5 (equation 2).
        1. If I solve equation (1) for x to get x = 4 − 3y and apply this to equation (2) to get 2(4 − 3y) + 3y = 5 (and continue from there), then what method am I using to solve this system?
        2. If instead I multiply equation (1) by −2 to get −2x − 6y = −8 and combine this with equation (2) to get −3y = −3 (and continue from there), then what method am I using to solve this system?
   • Exercises from the textbook due on August 26 Monday (submit these through MyLab): 11.1.3, 11.1.4, 11.1.6, 11.1.11, 11.1.13, 11.1.15, 11.1.17, 11.1.19, 11.1.21, 11.1.27, 11.1.31, 11.1.45, 11.1.47, 11.1.65, 11.1.73.
5. Systems of inequalities:
   • Reading: Section 11.7 (pages 794–799) from the textbook.
   • Exercises due on August 26 Monday (submit these on Canvas or in class):
     1. Fill in the blank: If a system of equations or inequalities has no solutions, then the system is _____.
     2. When graphing an inequality in two variables, if the inequality is strict (written with < or >, instead of ≤ or ≥), then should the boundary be solid or dashed?
   • Exercises from the textbook due on August 27 Tuesday (submit these through MyLab): 11.7.13, 11.7.14, 11.7.15, 11.7.23, 11.7.25, 11.7.27, 11.7.29, 11.7.31.
6. Functions:
   • Reading:
     • Section 2.1 (pages 47–59) from the textbook;
     • My online notes on functions.
   • Exercises due on August 27 Tuesday (submit these on Canvas or in class):
     1. Fill in the blank with a mathematical expression: If g(x) = 2x + 3 for all x, then g(___) = 2(5) + 3 = 13.
     2. Fill in the blank with an equation, inequality, or other statement: If a function f is thought of as a relation, then it's the relation {x, y | _____}.
     3. Fill in the blanks with vocabulary words: If f(3) = 5, then 3 belongs to the _____ of the function f, and 5 belongs to its _____.
     4. Fill in the blank with an arithmetic operation: If f(x) = 2x for all x, and g(x) = 3x for all x, then (f ___ g)(x) = 5x for all x.
   • Exercises from the textbook due on August 28 Wednesday (submit these through MyLab): 2.1.1, 2.1.2, 2.1.3, 2.1.10, 2.1.31, 2.1.33, 2.1.35, 2.1.37, 2.1.43, 2.1.49, 2.1.51, 2.1.53, 2.1.55, 2.1.59, 2.1.63, 2.1.71, 2.1.79, 2.1.81, 2.1.103.
7. Graphs of functions:
   • Reading: Section 2.2 (pages 63–67) from the textbook.
   • Exercises due on August 28 Wednesday (submit these on Canvas or in class):
     1. Fill in the blanks with mathematical expressions: If (3, 5) is a point on the graph of a function f, then f(___) = ___.
     2. Fill in the blank with a geometric word: The graph of a relation is the graph of a function if and only if every _____ line goes through the graph at most once.
     3. Which of these is true, and which of these is false?
        1. The graph of a function can have any number of x-intercepts;
        2. The graph of a function can have any number of y-intercepts.
   • Exercises from the textbook due on August 29 Thursday (submit these through MyLab): 2.2.7, 2.2.9, 2.2.11, 2.2.13, 2.2.15, 2.2.17, 2.2.19, 2.2.21, 2.2.27, 2.2.29, 2.2.31, 2.2.33, 2.2.39, 2.2.45, 2.2.47.
8. Properties of functions:
   • Reading:
     • Section 2.3 (pages 73–81) from the textbook;
     • My online notes on properties of functions.
   • Exercises due on August 29 Thursday (submit these on Canvas or in class): Fill in the blanks with vocabulary words:
     1. Suppose that f is a function and, whenever f(x) exists, then f(−x) also exists and equals f(x). Then f is _____.
     2. If c is a number and f is a function, and if f(c) = 0, then c is a(n) _____ of f.
     3. Suppose that a function f is defined on (at least) a nontrivial interval I and that, whenever a ∈ I and b ∈ I, if a < b, then f(a) < f(b). Then f is (strictly) _____ on I.
   • Exercises from the textbook due on August 30 Friday (submit these through MyLab): 2.3.2, 2.3.3, 2.3.5, 2.3.13, 2.3.15, 2.3.17, 2.3.19, 2.3.21, 2.3.23, 2.3.26, 2.3.27, 2.3.29, 2.3.31, 2.3.37, 2.3.39, 2.3.41, 2.3.43, 2.3.45, 2.3.49, 2.3.51.
9. Word problems with functions:
   • Reading:
     • Section 2.6 (pages 111–113) from the textbook;
     • My online notes and video on functions in word problems.
   • Exercise due on August 30 Friday (submit this on Canvas or in class): Suppose that you have a problem with three quantities, A, B, and C; and suppose that you have two equations, equation (1) involving A and B, and equation (2) involving B and C. If you wish to find A as a function of C, then which equation should you solve first, and which variable should you solve it for? (Although there is a single best answer in my opinion, there is more than one answer that will progress the solution, and I'll accept either of them.)
   • Exercises from the textbook due on September 3 Tuesday (submit these through MyLab): 2.6.5, 2.6.13, 2.6.15, 2.6.21, 2.6.23.

Operations on functions

10. Linear functions:
    • Reading: Section 3.1 (pages 125–131) from the textbook.
    • Exercises due on September 3 Tuesday (submit these on Canvas or in class):
      1. Suppose that y is a linear function of x. If the rate of change of the function is m and the initial value of the function is b, then write an equation relating x and y.
      2. Suppose that f is a linear function. If you know f(x₁) and f(x₂) for two distinct real numbers x₁ and x₂, then give a formula for the slope of the graph of f using x₁, x₂, f(x₁), and/or f(x₂).
    • Exercises from the textbook due on September 4 Wednesday (submit these through MyLab): 3.1.2, 3.1.13, 3.1.15, 3.1.17, 3.1.19, 3.1.21, 3.1.23, 3.1.25, 3.1.27, 3.1.37, 3.1.43, 3.1.45, 3.1.47, 3.1.49.
11. Examples of functions:
    • Reading:
      • Section 2.4 through Objective 1 (pages 86–90) from the textbook;
      • My online notes and video on partially-defined functions;
      • The rest of Section 2.4 (pages 91–93) from the textbook.
    • Exercises due on September 4 Wednesday (submit these on Canvas or in class): Fill in the blanks with vocabulary words:
      1. In the _____ function, the output is always defined and equal to the input.
      2. A _____-defined function is defined by a formula together with a condition restricting its inputs.
      3. A _____-defined function is defined by more than one formula, each with a condition restricting its inputs.
    • Exercises from the textbook due on September 5 Thursday (submit these through MyLab): 2.4.9, 2.4.10, 2.4.11–18, 2.4.19, 2.4.20, 2.4.21, 2.4.22, 2.4.23, 2.4.24, 2.4.25, 2.4.26, 2.4.27, 2.4.29, 2.4.31, 2.4.33, 2.4.35, 2.4.43, 2.4.45, 2.4.51.
12. Composite functions:
    • Reading:
      • Most of Section 5.1 (pages 259–263) from the textbook;
      • My online notes on composite functions.
    • Exercises due on September 5 Thursday (submit these on Canvas or in class):
      1. Fill in the blanks with a vocabulary word and a mathematical expression: If f and g are functions, then their _____ function, denoted f ∘ g, is defined by (f ∘ g)(x) = _____.
      2. Fill in the blanks with mathematical expressions: A number x is in the domain of f ∘ g if and only if ___ belongs to the domain of g and ___ belongs to the domain of f.
    • Exercises from the textbook due on September 6 Friday (submit these through MyLab): 5.1.2, 5.1.9, 5.1.11, 5.1.15, 5.1.19, 5.1.25, 5.1.27, 5.1.29, 5.1.33, 5.1.55.
13. Inverse functions:
    • Reading:
      • Section 5.2 (pages 267–274) from the textbook;
      • My online notes on inverse functions.
    • Exercises due on September 10 Tuesday (submit these on Canvas or in class):
      1. Fill in the blank with a geometric word: A function is one-to-one if and only if every _____ line goes through its graph at most once.
      2. Fill in the blank with a vocabulary word: If f is a one-to-one function, then its _____ function, denoted f⁻¹, exists.
      3. Fill in the blank with an ordered pair: If f is one-to-one and (2, −3) is on the graph of f, then ___ is on the graph of f⁻¹.
    • Exercises from the textbook due on September 11 Wednesday (submit these through MyLab): 5.2.4, 5.2.5, 5.2.7, 5.2.8, 5.2.9, 5.2.12, 5.2.21, 5.2.23, 5.2.25, 5.2.27, 5.2.29, 5.2.31, 5.2.35, 5.2.37, 5.2.41, 5.2.43, 5.2.45, 5.2.55, 5.2.57, 5.2.59, 5.2.61, 5.2.75, 5.2.77, 5.2.79, 5.2.87.
14. Coordinate transformations:
    • Reading:
      • Section 2.5 (pages 98–107) from the textbook;
      • My online notes on linear coordinate transformations.
    • Exercises due on September 11 Wednesday (submit these on Canvas or in class): Assume that the axes are oriented in the usual way (positive x-axis to the right, positive y-axis upwards).
      1. Fill in the blank with a direction: To change the graph of y = f(x) into the graph of y = f(x − 1), shift the graph to the ___ by 1 unit.
      2. To change the graph of y = f(x) into the graph of y = −f(x), do you reflect the graph left and right or up and down?
      3. To change the graph of y = f(x) into the graph of y = f(2x), do you compress or stretch the graph left and right?
    • Exercises from the textbook due on September 12 Thursday (submit these through MyLab): 2.5.5, 2.5.6, 2.5.7–10, 2.5.11–14, 2.5.15–18, 2.5.19, 2.5.21, 2.5.23, 2.5.25, 2.5.29, 2.5.30, 2.5.33, 2.5.35, 2.5.37, 2.5.41, 2.5.43, 2.5.45, 2.5.47, 2.5.53, 2.5.61, 2.5.63, 2.5.73, 2.5.89.
15. Quadratic functions:
    • Reading:
      • Section 3.3 (pages 143–152) from the textbook;
      • My online notes on quadratic functions.
    • Exercises due on September 12 Thursday (submit these on Canvas or in class):
      1. Fill in the blank with a vocabulary word: The shape of the graph of a nonlinear quadratic function is a(n) _____.
      2. Fill in the blanks with algebraic expressions: Given a ≠ 0 and f(x) = ax² + bx + c for all x, the vertex of the graph of f is (___, ___).
      3. Given a ≠ 0, b² − 4ac > 0, and f(x) = ax² + bx + c for all x, how many x-intercepts does the graph of y = f(x) have?
    • Exercises from the textbook due on September 13 Friday (submit these through MyLab): 3.3.1, 3.3.2, 3.3.3, 3.3.4, 3.3.15–22, 3.3.31, 3.3.33, 3.3.43, 3.3.49, 3.3.53, 3.3.57, 3.3.61, 3.3.63, 3.3.67, 3.3.70.
16. Applications of quadratic functions:
    • Reading:
      • Section 3.4 through Objective 1 (pages 156–160) from the textbook;
      • My online notes on economic applications.
    • Exercises due on September 13 Friday (submit these on Canvas or in class):
      1. Suppose that x and y are variables, x can take any value, and y = ax² + bx + c for some constants a, b, and c.
         1. Fill in the blank with an algebraic equation or inequality: y has a maximum value if _____.
         2. Fill in the blank with an algebraic expression: In this case, y has its maximum when x = ___.
      2. If the width of a rectangle is w metres and its length is l metres, then what is its area (in square metres)?
      3. If you make and sell x items per year at a price of p dollars per item, then what is your revenue (in dollars per year)?
      4. If a business's revenue is R dollars per year and its costs are C dollars per year, then what is its profit (in dollars per year)?
    • Exercises from the textbook due on September 16 Monday (submit these through MyLab): 3.3.87, 3.3.89, 3.3.93, 3.3.95, 3.4.3, 3.4.5, 3.4.7, 3.4.9, 3.4.11, 3.4.13, 3.4.15.
17. Power functions:
    • Reading:
      • My online notes on power functions;
      • Section 4.1 through Objective 2 (pages 175–180) from the textbook.
    • Exercises due on September 16 Monday (submit these on Canvas or in class): Give the coordinates of:
      1. A point on the graph of every power function.
      2. Another point (different from the answer to #1) on the graph of every power function with a positive exponent.
      3. Another point on the graph of every power function with an even exponent.
      4. Another point on the graph of every power function with an odd exponent.
    • Exercises from the textbook due on September 17 Tuesday (submit these through MyLab): 4.1.2, 4.1.15, 4.1.17, 4.1.19, 4.1.21, 4.1.27, 4.1.29, 4.1.33.
18. Graphing polynomials:
    • Reading:
      • The rest of Section 4.1 (pages 180–186) from the textbook;
      • My online notes on graphing polynomials (but the last paragraph is optional);
      • Section 4.2 through Objective 1 (pages 190–192) from the textbook.
    • Exercises due on September 17 Tuesday (submit these on Canvas or in class):
      1. If a root (aka zero) of a polynomial function has odd multiplicity, then does the graph cross (go through) or only touch (bounce off) the horizontal axis at the intercept given by that root? Which does the graph do if the root has even multiplicity?
      2. If the leading coefficient of a polynomial function is positive, then does the graph's end behaviour go up on the far right, or down? Which does the graph do if the leading coefficient is negative?
    • Exercises from the textbook due on September 18 Wednesday (submit these through MyLab): 4.1.1, 4.1.11, 4.1.41, 4.1.43, 4.1.47, 4.1.49, 4.1.59, 4.1.61, 4.1.69, 4.1.71, 4.1.73, 4.1.75, 4.2.1, 4.2.2, 4.2.5, 4.2.11.

Rational and logarithmic functions

19. Advanced factoring:
    • Reading:
      • Section A.4 (pages A31–A34) from the textbook;
      • Section 4.6 through Objective 1 (pages 231–234) from the textbook;
      • Section 4.6 Objectives 3–5 (pages 235–239) from the textbook.
    • Exercises due on September 18 Wednesday (submit these on Canvas or in class):
      1. Suppose that f is a polynomial function and c is a number. If you divide f(x) by x − c, then what will the remainder be?
      2. Suppose that f is a polynomial function with rational coefficients and c is an integer. If x − c is a factor of f(x), then what is f(c)?
    • Exercises from the textbook due on September 19 Thursday (submit these through MyLab): 4.6.2, 4.6.3, 4.6.4, 4.6.11, 4.6.15, 4.6.19, 4.6.33, 4.6.35, 4.6.37, 4.6.45, 4.6.51, 4.6.53, 4.6.57, 4.6.59, 4.6.65, 4.6.67, 4.6.93, 4.6.99, 4.6.101.
20. Imaginary roots:
    • Reading: Section 4.7 (pages 245–250) from the textbook.
    • Exercises due on September 19 Thursday (submit these on Canvas or in class): Suppose that f is a polynomial function with real coefficients, a and b are real numbers with b ≠ 0, and the imaginary complex number a + bi is a root (or zero) of f.
      1. What other complex number must be a root of f?
      2. What non-constant polynomial in x (with real coefficients) must be a factor of f(x)?
    • Exercises from the textbook due on September 20 Friday (submit these through MyLab): 4.7.1, 4.7.2, 4.7.9, 4.7.11, 4.7.13, 4.7.15, 4.7.17, 4.7.19, 4.7.21, 4.7.23, 4.7.25, 4.7.29, 4.7.35, 4.7.39.
21. Rational functions:
    • Reading:
      • Section 4.3 (pages 198–205) from the textbook;
      • Section 4.4 (pages 209–219) from the textbook;
      • My online notes on rational functions.
    • Exercises due on September 24 Tuesday (submit these on Canvas or in class):
      1. If a graph gets arbitrarily close to a line (without necessarily reaching it) in some direction, then the line is a(n) _____ of the graph.
      2. If the reduced form of a rational function is defined somewhere where the original (unreduced) form is not, then the graph of the original function has a(n) _____ there.
      3. Suppose that when you divide R(x) = P(x)/Q(x), you get a linear quotient q(x) and a linear remainder r(x).
         1. Write an equation in x and y for the non-vertical linear asymptote of the graph of R.
         2. Write an equation in x that you might solve to find where the graph of R meets this asymptote.
         (Warning: Don't mix up lowercase and uppercase letters in your answer!)
    • Exercises from the textbook due on September 25 Wednesday (submit these through MyLab): 4.3.2, 4.3.3, 4.3.4, 4.3.15, 4.3.17, 4.3.19, 4.3.23, 4.3.27, 4.3.29, 4.3.31, 4.3.35, 4.3.45, 4.3.47, 4.3.49, 4.3.51, 4.4.1, 4.4.5, 4.4.7, 4.4.9, 4.4.11, 4.4.17, 4.4.19, 4.4.21, 4.4.23, 4.4.31, 4.4.33, 4.4.35, 4.4.51, 4.4.53.
22. Inequalities:
    • Reading:
      • Section 4.5 (pages 224–228) from the textbook;
      • My online notes on solving inequalities.
    • Exercise due on September 25 Wednesday (submit this on Canvas or in class): Suppose that you have a rational inequality in the variable x that you wish to solve. You investigate the inequality and discover the following facts about it:
      • the left-hand side is always defined;
      • the right-hand side is undefined when x is 2 but is otherwise defined;
      • the two sides are equal when x is −3/2 and only then;
      • the original inequality is true when x is −3/2 or 3 but false when x is −2, 0, or 2.
      What are the solutions to the inequality?
    • Exercises from the textbook due on September 26 Thursday (submit these through MyLab): 4.5.1, 4.5.5, 4.5.7, 4.5.9, 4.5.13, 4.5.15, 4.5.19, 4.5.21, 4.5.23, 4.5.27, 4.5.29, 4.5.35, 4.5.39, 4.5.41, 4.5.43, 4.5.47.
23. Exponential functions:
    • Reading:
      • Section 5.3 (pages 279–290) from the textbook;
      • My online notes on exponential functions.
    • Exercises due on September 26 Thursday (submit these on Canvas or in class): Let f(x) be Cb^x for all x.
      1. What is f(x + 1)/f(x)?
      2. What are f(−1), f(0), and f(1)?
      (Write your answers using b and C, and simplify them as much as possible.)
    • Exercises from the textbook due on September 27 Friday (submit these through MyLab): 5.3.1, 5.3.15, 5.3.16, 5.3.21, 5.3.23, 5.3.25, 5.3.27, 5.3.29, 5.3.31, 5.3.33, 5.3.35, 5.3.37–44, 5.3.45, 5.3.47, 5.3.51, 5.3.53, 5.3.57, 5.3.59, 5.3.61, 5.3.65, 5.3.67, 5.3.71, 5.3.73, 5.3.76, 5.3.77, 5.3.79, 5.3.83, 5.3.85, 5.3.91, 5.3.93.
24. Logarithmic functions:
    • Reading:
      • Section 5.4 (pages 296–304) from the textbook;
      • My online notes on logarithmic functions.
    • Exercises due on September 27 Friday (submit these on Canvas or in class): Suppose that b > 0 and b ≠ 1.
      1. Rewrite log_b M = r as an equation involving exponentiation.
      2. What are log_b b, log_b 1, and log_b(1/b)?
    • Exercises from the textbook due on September 30 Monday (submit these through MyLab): 5.4.11, 5.4.13, 5.4.15, 5.4.17, 5.4.19, 5.4.21, 5.4.23, 5.4.25, 5.4.27, 5.4.29, 5.4.31, 5.4.33, 5.4.35, 5.4.37, 5.4.39, 5.4.43, 5.4.51, 5.4.53, 5.4.55, 5.4.57, 5.4.65–72, 5.4.73, 5.4.79, 5.4.83, 5.4.85, 5.4.89, 5.4.91, 5.4.93, 5.4.95, 5.4.97, 5.4.99, 5.4.101, 5.4.103, 5.4.105, 5.4.107, 5.4.109, 5.4.111, 5.4.119, 5.4.129, 5.4.131.
25. Properties of logarithms:
    • Reading:
      • Section 5.5 (pages 309–315) from the textbook;
      • My online notes on laws of logarithms.
    • Exercises due on September 30 Monday (submit these on Canvas or in class):
      1. Fill in the blanks to break down these expressions using properties of logarithms. (Assume that b, u, and v are all positive and that b ≠ 1.)
         1. log_b(uv) = ___;
         2. log_b(u/v) = ___;
         3. log_b(u^x) = ___.
      2. Given b > 0, b ≠ 1, and u > 0, write log_b u in these two ways:
         1. Using only common logarithms (logarithms base 10);
         2. Using only natural logarithms (logarithms base e).
    • Exercises from the textbook due on October 1 Tuesday (submit these through MyLab): 5.5.7, 5.5.11, 5.5.13, 5.5.15, 5.5.17, 5.5.19, 5.5.21, 5.5.23, 5.5.25, 5.5.27, 5.5.37, 5.5.39, 5.5.41, 5.5.43, 5.5.45, 5.5.47, 5.5.49, 5.5.51, 5.5.53, 5.5.55, 5.5.57, 5.5.61, 5.5.63, 5.5.65, 5.5.67, 5.5.69, 5.5.71, 5.5.73, 5.5.75, 5.5.78, 5.5.87, 5.5.91, 5.5.97.
26. Logarithmic equations:
    • Reading: Section 5.6 through Objective 2 (pages 318–321) from the textbook.
    • Exercises due on October 1 Tuesday (submit these on Canvas or in class): In solving which of the following equations would it be useful to have a step in which you take logarithms of both sides of the equation? (Say Yes or No for each one.)
      1. log₂(x + 3) = 5;
      2. (x + 3)² = 5;
      3. 2^{x + 3} = 5.
    • Exercises from the textbook due on October 2 Wednesday (submit these through MyLab): 5.6.1, 5.6.2, 5.6.5, 5.6.7, 5.6.9, 5.6.15, 5.6.19, 5.6.21, 5.6.23, 5.6.25, 5.6.27, 5.6.29, 5.6.31, 5.6.39, 5.6.43, 5.6.45, 5.6.49, 5.6.57, 5.6.61.
27. Compound interest:
    • Reading:
      • Section 5.7 (pages 325–331) from the textbook;
      • My online notes on compound interest.
    • Exercises due on October 2 Wednesday (submit these on Canvas or in class):
      1. The original amount of money that earns interest is the _____.
      2. If you borrow P dollars at 100r% annual interest compounded n times per year, then how much will you owe after t years (if you make no payments)?
    • Exercises from the textbook due on October 3 Thursday (submit these through MyLab): 5.7.1, 5.7.2, 5.7.7, 5.7.11, 5.7.13, 5.7.15, 5.7.21, 5.7.31, 5.7.33, 5.7.41, 5.7.43.
28. Applications of logarithms:
    • Reading:
      • Section 5.8 (pages 335–342) from the textbook;
      • My online notes on applications of logarithms.
    • Exercises due on October 3 Thursday (submit these on Canvas or in class):
      1. Suppose that a quantity A undergoes exponential growth with a relative growth rate of k and an initial value of A₀ at time t = 0. Write down a formula for the value of A as a function of the time t.
      2. Suppose that a quantity A undergoes exponential decay with a halflife of h and an initial value of A₀ at time t = 0. Write down a formula for the value of A as a function of the time t.
    • Exercises from the textbook due on October 4 Friday (submit these through MyLab): 5.8.1, 5.8.3, 5.8.5, 5.8.7, 5.8.9, 5.8.11, 5.8.13, 5.8.15, 5.8.17, 5.8.19, 5.8.21, 5.8.23.

Trigonometric functions

29. Circles:
    • Reading: Section 1.4 (pages 35–39) from the textbook.
    • Exercises due on October 4 Friday (submit these on Canvas or in class):
      1. Fill in the blank: The distance from the centre (or center) of a circle to any point on the circle is the _____ of the circle.
      2. Write down an equation in the variables x and y for a circle whose centre is (h, k) and whose radius is r. (This will be an equation in which x, y, h, k, and r all appear.)
      3. If x² + y² = r² is the equation of a circle in x and y, then what are the coordinates of the centre of the circle?
    • Exercises from the textbook due on October 7 Monday (submit these through MyLab): 1.4.5, 1.4.9, 1.4.11, 1.4.13, 1.4.15, 1.4.17, 1.4.21, 1.4.23, 1.4.25, 1.4.27.
30. Angles:
    • Reading: Section 6.1 through Objective 4 (pages 362–368) from the textbook.
    • Exercises due on October 7 Monday (submit these on Canvas or in class):
      1. If a central angle in a circle subtends an arc whose length equals the circle's radius, then what is the measure of that angle?
      2. How many radians is 360°?
    • Exercises from the textbook due on October 8 Tuesday (submit these through MyLab): 6.1.11, 6.1.13, 6.1.15, 6.1.17, 6.1.19, 6.1.21, 6.1.23, 6.1.26, 6.1.35, 6.1.37.
31. Length and area with radians:
    • Reading: The rest of Section 6.1 (pages 368–370) from the textbook.
    • Exercises due on October 8 Tuesday (submit these on Canvas or in class): Fill in the blanks with algebraic expressions:
      1. In a circle of radius r, a central angle whose measure is θ radians subtends an arc whose length is s = ___.
      2. In a circle of radius r, a central angle whose measure is θ forms a sector whose area is A = ___.
      3. Around a circle of radius r, an object with an angular speed of ω has a linear speed of v = ___.
    • Exercises from the textbook due on October 9 Wednesday (submit these through MyLab): 6.1.71, 6.1.73, 6.1.79, 6.1.81, 6.1.87, 6.1.91, 6.1.95, 6.1.99.
32. The trigonometric operations:
    • Reading:
      • Section 6.2 through Objective 2 (pages 375–380) from the textbook;
      • Section 6.2 Objectives 6&7 (pages 385–387) from the textbook.
    • Exercises due on October 9 Wednesday (submit these on Canvas or in class):
      1. Suppose that you start at the point (1, 0) in a rectangular coordinate system and move in the direction towards (0, 1) along the unit circle, for a total distance t. (This is the usual thing, not a trick question.) If you end at the point (x, y), express sin t, cos t, tan t, cot t, sec t, and csc t using only x and y.
      2. Now instead of moving along the unit circle (with radius 1), move along a circle of radius r (but still centred at the origin). That is, start at (r, 0) and move along the circle in the direction of (0, r) for a total distance of s, and let θ be s/r. (This is again the usual thing for a non-unit radius.) Now if you end at the point (x, y), express sin θ, cos θ, tan θ, cot θ, sec θ, and csc θ using only x, y, and r.
      3. If you want to calculate the secant of 50 degrees on a calculator with buttons only for sine, cosine, and tangent, then what do you enter on the calculator?
    • Exercises from the textbook due on October 10 Thursday (submit these through MyLab): 6.2.13, 6.2.15, 6.2.17, 6.2.19, 6.2.65, 6.2.67, 6.2.69, 6.2.71, 6.2.77, 6.2.79.
33. Right triangles:
    • Reading: Section 8.1 through Objective 2 (pages 522–524) from the textbook.
    • Exercises due on October 10 Thursday (submit these on Canvas or in class):
      1. If θ is the measure of an acute angle in a right triangle, then express the six basic trigonometric functions of θ as ratios of the lengths of the adjacent leg, the opposite leg, and the hypotenuse.
      2. Fill in the blank: The sine of the complement of θ is the _____ of θ.
    • Exercises from the textbook due on October 11 Friday (submit these through MyLab): 8.1.9, 8.1.11, 8.1.13, 8.1.19, 8.1.21, 8.1.23.
34. Special angles:
    • Reading: The rest of Section 6.2 (pages 380–385) from the textbook.
    • Exercises due on October 17 Thursday (submit these on Canvas or in class):
      1. Write down the exact values of the sine, cosine, tangent, cotangent, secant, and cosecant of 0, π/6, π/4, π/3, and π/2. (This is 30 values to write down in all, which you might put into a handy table. One way or another, be sure to label which value is which.)
      2. For each of Quadrants I, II, III, and IV, which of the six fundamental trigonometric functions of θ are positive and which are negative when θ terminates in that quadrant? (This is 24 positive/negative answers in all, which you might also put into a table.)
    • Exercises from the textbook due on October 18 Friday (submit these through MyLab): 6.2.31, 6.2.33, 6.2.35, 6.2.41, 6.2.43, 6.2.45, 6.2.47, 6.2.49, 6.2.51, 6.2.53, 6.2.55, 6.3.11, 6.3.19, 6.3.31.
35. The trigonometric functions:
    • Reading: Section 6.3 (pages 392–403) from the textbook.
    • Exercises due on October 18 Friday (submit these on Canvas or in class):
      1. Most of the six trigonometric functions have a period of 2π; which two have a period of π instead?
      2. Consider the numbers 2 and 1/2. Which is in the range of the sine function, and which is in the range of the cosecant function?
      3. Out of 0, π/2, π, and 2π, which is not in the domain of the tangent function?
    • Exercises from the textbook due on October 21 Monday (submit these through MyLab): 6.4.3, 6.3.35, 6.3.37, 6.3.43, 6.3.45, 6.3.53, 6.3.55, 6.3.89, 6.3.115.
36. Basic sinusoidal graphs:
    • Reading:
      • Section 6.4 through the box before Example 1 (pages 407&408) from the textbook;
      • Section 6.4 Objective 2 through the box before Example 3 (pages 409&410) from the textbook.
    • Exercises due on October 21 Monday (submit these on Canvas or in class):
      1. List at least five consecutive horizontal intercepts of the graph of the sine function.
      2. Give the vertical intercept of the graph of the sine function.
      3. List at least five consecutive turning points of the graph of the sine function.
      4. List at least five consecutive horizontal intercepts of the graph of the cosine function.
      5. Give the vertical intercept of the graph of the cosine function.
      6. List at least five consecutive turning points of the graph of the cosine function.
    • Exercises from the textbook due on October 22 Tuesday (submit these through MyLab): 6.4.6, 6.4.8, 6.4.11, 6.4.13.
37. More basic graphs:
    • Reading:
      • Section 6.5 through "The Graph of the Cotangent Function y = cot x" (pages 422–424) from the textbook;
      • Section 6.5 Objective 3 (pages 425&426) from the textbook.
    • Exercises due on October 22 Tuesday (submit these on Canvas or in class):
      1. List at least five consecutive horizontal intercepts of the graph of the tangent function.
      2. List at least five consecutive linear asymptotes of the graph of the tangent function.
      3. List at least five consecutive horizontal intercepts of the graph of the cotangent function.
      4. List at least five consecutive linear asymptotes of the graph of the cotangent function.
      5. List at least five consecutive linear asymptotes of the graph of the secant function.
      6. List at least five consecutive linear asymptotes of the graph of the cosecant function.
    • Exercises from the textbook due on October 23 Wednesday (submit these through MyLab): 6.5.3, 6.5.6, 6.5.7, 6.5.10, 6.5.11, 6.5.12, 6.5.13, 6.5.16.

Analytic trigonometry

38. Transformations of trigonometric functions:
    • Reading:
      • Section 6.4 Objective 1 Examples 1&2 (pages 408&409) from the textbook;
      • Section 6.4 Objective 2 Example 3 (page 410) from the textbook;
      • Section 6.5 Objective 2 (pages 424&425) from the textbook;
      • Section 6.5 Objective 4 (pages 426&427) from the textbook.
    • Exercises due on October 23 Wednesday (submit these on Canvas or in class): Suppose that f is a periodic function with period T. (For example, f might be the sine function, so that T would be 2π, or f might be the tangent function, so that T would be π. But answer the questions in general, referring to T.)
      1. What is the period (in x) of f(x + 2)?
      2. What is the period of f(2x)?
      3. What is the period of 2f(x)?
    • Exercises from the textbook due on October 24 Thursday (submit these through MyLab): 6.4.23–32, 6.5.17, 6.5.21, 6.5.23, 6.5.25, 6.5.29, 6.5.31.
39. Sinusoidal functions:
    • Reading:
      • My handout on sinusoidal functions (DjVu TBA);
      • The rest of Section 6.4 (pages 410–416) from the textbook;
      • Section 6.6 Objective 1 (pages 429–433) from the textbook.
    • Exercises due on October 24 Thursday (submit these on Canvas or in class):
      1. If f(x) = A sin(ωx) for all x, with A > 0 and ω > 0, then what are the amplitude and period of f?
      2. If f(x) = A sin x + B for all x, with A > 0, then what are the maximum and minimum values of f?
      3. If f(x) = sin(ωx − φ) for all x, with ω > 0 and 0 ≤ φ < 2π, then what is the phase shift of f?
    • Exercises from the textbook due on October 25 Friday (submit these through MyLab): 6.4.35, 6.4.39, 6.4.51, 6.4.57, 6.4.61, 6.4.87, 6.6.9, 6.6.11, 6.6.17, 6.6.19.
40. Inverse trigonometric operations:
    • Reading:
      • Section 7.1 through Objective 7 (pages 450–458) from the textbook;
      • Section 7.2 through Objective 2 (pages 463–465) from the textbook.
    • Exercises due on October 29 Tuesday (submit these on Canvas or in class): Fill in all of these blanks with algebraic expressions (or constants). Work only in the real number system.
      1. That y = sin⁻¹ x means that x = ___ and ___ ≤ y ≤ ___.
      2. cos⁻¹ x exists if and only if ___ ≤ x ≤ ___.
      3. cos⁻¹ cos θ = θ if and only if ___ ≤ θ ≤ ___.
    • Exercises from the textbook due on October 30 Wednesday (submit these through MyLab): 7.1.19, 7.1.21, 7.2.11, 7.2.13, 7.2.19, 7.1.39, 7.1.41, 7.1.43, 7.1.45, 7.1.51, 7.1.53, 7.1.55, 7.1.57.
41. More inverse trigonometric operations:
    • Reading:
      • The rest of Section 7.1 (pages 458&459) from the textbook;
      • The rest of Section 7.2 (pages 465&466) from the textbook;
      • My handout on inverse trigonometric operations (DjVu).
    • Exercises due on October 30 Wednesday (submit these on Canvas or in class):
      1. Fill in the blank with an algebraic expression: cos sin⁻¹ x = ___ (if either side exists in the real number system).
      2. If f is the function given by f(x) = sin⁻¹ x, then what is its inverse function f ⁻¹? (Write down a formula that involves one or more of the six basic trigonometric operations and that includes all necessary conditions.)
    • Exercises from the textbook due on October 31 Thursday (submit these through MyLab): 7.2.33, 7.2.35, 7.2.47, 7.2.49, 7.1.59, 7.1.61, 7.2.61, 7.2.63, 7.2.65.
42. Sum-angle formulas:
    • Reading:
      • Section 7.5 through Objective 3 (pages 487–494) from the textbook;
      • Section 7.6 through the paragraph with the footnote following Example 2 in Objective 2 (pages 500–502) from the textbook.
    • Exercises due on October 31 Thursday (submit these on Canvas or in class): Fill in the blanks with trigonometric expressions in which each trigonometric operation that appears is only applied directly to α or β.
      1. sin(α + β) = ___.
      2. cos(α + β) = ___.
      3. sin(α − β) = ___.
      4. tan(α + β) = ___.
      5. sin(2α) = ___.
    • Exercises from the textbook due on November 1 Friday (submit these through MyLab): 7.5.15, 7.5.17, 7.5.19, 7.5.21, 7.5.35, 7.5.37, 7.5.39, 7.5.41, 7.5.77, 7.6.83, 7.6.85, 7.6.87.
43. Sum-product formulas:
    • Reading:
      • The rest of Section 7.6 Objective 2 through Example 3 (pages 502&503) from the textbook;
      • Section 7.7 (pages 511–513) from the textbook.
    • Exercises due on November 1 Friday (submit these on Canvas or in class):
      1. Express sin² α using sin(2α) and/or cos(2α).
      2. Express sin α sin β using sin(α + β), sin(α − β), cos(α + β), and/or cos(α − β).
      3. Factor sin α + sin β so that each factor has at most one trigonometric operation.
    • Exercises from the textbook due on November 4 Monday (submit these through MyLab): 7.7.7, 7.7.9, 7.7.11, 7.7.13, 7.7.15, 7.7.17, 7.7.19, 7.7.21, 7.7.23.
44. Half-angle formulas:
    • Reading: Section 7.6 Objective 3 (pages 504–506) from the textbook.
    • Exercises due on November 4 Monday (submit these on Canvas or in class): Fill in the blanks with trigonometric expressions in which each trigonometric operation that appears is only applied directly to α. Make sure that each expression has at most one value for each value of α; in other words, do not use ±.
      1. sin²(α/2) = ___.
      2. cos²(α/2) = ___.
      3. tan(α/2) = ___ (notice not squared).
    • Exercises from the textbook due on November 5 Tuesday (submit these through MyLab): 7.6.25, 7.6.29, 7.6.23, 7.6.27, 7.6.9, 7.6.11, 7.6.13, 7.6.15, 7.6.17, 7.6.19.
45. Simplifying trigonometric expressions:
    • Reading:
      • My handout on simplifying trigonometric expressions (DjVu);
      • Section 7.4 (pages 479–484) from the textbook.
    • Exercises due on November 5 Tuesday (submit these on Canvas or in class):
      1. Fill in the blank with an expression in which sin θ is the only trigonometric quantity: cos² θ = ___.
      2. Factor without using any trigonometric identities: sin² θ − 1 = (___)(___).
      3. If you regard a cosine as a square root, then what expression is conjugate to 1 − cos θ? (Hint: If you were to multiply these conjugate expressions together, then θ would appear only as cos² θ.)
    • Exercises from the textbook due on November 6 Wednesday (submit these through MyLab): 7.4.1, 7.4.2, 7.4.6, 7.4.8, 7.4.11, 7.4.15, 7.4.17, 7.4.29, 7.4.55, 7.4.71, 7.4.95.
46. Trigonometric equations:
    • Reading: Section 7.3 (pages 469–474) from the textbook.
    • Exercises due on November 6 Wednesday (submit these on Canvas or in class):
      1. Write a general form for the solutions of tan x = b using tan⁻¹ b and an arbitrary integer k.
      2. Similarly, give the general solution of sin x = b. (This one is more complicated than the last one.)
      3. To obtain θ ∈ [0, 2π) (that is, 0 ≤ θ < 2π), what interval should 3θ belong to?
    • Exercises from the textbook due on November 7 Thursday (submit these through MyLab): 7.3.13, 7.3.23, 7.3.25, 7.3.27, 7.3.37, 7.3.39, 7.3.115.
47. Tricky trigonometric equations:
    • Reading:
      • Section 7.5 Objective 4 (pages 494–496) from the textbook;
      • Section 7.6 Objective 2 Examples 4&5 (pages 503&504) from the textbook.
    • Exercises due on November 7 Thursday (submit these on Canvas or in class):
      1. Since you can factor x + xy as x(1 + y), how can you factor cos θ + sin θ cos θ?
      2. To solve a sin θ + b cos θ = c with the help of a sum-angle formula, what should you multiply both sides of the equation by?
      3. To solve sin(aθ) + sin(bθ) = 0, how can you factor the left-hand side?
    • Exercises from the textbook due on November 8 Friday (submit these through MyLab): 7.3.61, 7.3.73, 7.5.93, 7.5.97, 7.6.75, 7.6.77, 7.7.47.

Applications of trigonometry

48. Solving right triangles:
    • Reading: Section 8.1 Objective 3 (pages 524&525) from the textbook.
    • Exercises due on November 12 Tuesday (submit these on Canvas or in class):
      1. Answer this in degrees, and also answer it in radians: If A and B are the two acute angles in a right triangle, then A + B = ___.
      2. True or false: Knowing any two of the three sides of a right triangle is enough information to solve the triangle completely.
      3. True or false: Knowing any two of the three angles of a right triangle is enough information to solve the triangle completely.
    • Exercises from the textbook due on November 13 Wednesday (submit these through MyLab): 8.1.2, 8.1.29, 8.1.31, 8.1.33, 8.1.35, 8.1.37, 8.1.39, 8.1.41.
49. The Law of Sines:
    • Reading: Section 8.2 through Objective 2 (pages 535–539) from the textbook.
    • Exercises due on November 13 Wednesday (submit these on Canvas or in class): In each of the following forms of the Law of Sines, fill in the blank to get a true theorem (where a, b and c are the lengths of the three sides of a triangle and A, B, and C are the measures of the respective opposite angles).
      1. a ÷ sin A = b ÷ ___.
      2. b ÷ c = sin B ÷ ___.
      3. sin A ÷ a = sin C ÷ ___.
    • Exercises from the textbook due on November 14 Thursday (submit these through MyLab): 8.2.9, 8.2.11, 8.2.13, 8.2.15, 8.2.18, 8.2.27, 8.2.29, 8.2.33, 8.2.35, 8.2.37.
50. The Law of Cosines:
    • Reading:
      • Section 8.3 through Objective 2 (pages 546–548) from the textbook;
      • My handout on solving triangles (DjVu).
    • Exercises due on November 14 Thursday (submit these on Canvas or in class):
      1. Which law do you use to solve a triangle, if you are given two angles and one of the sides?
      2. Which law do you use if you are given the three sides?
      3. What do you do if you are given only the angles?
    • Exercises from the textbook due on November 15 Friday (submit these through MyLab): 8.3.9, 8.3.11, 8.3.13, 8.3.15, 8.3.35, 8.3.37, 8.3.41, 8.3.43.
51. Area of triangles:
    • Reading: Section 8.4 (pages 553–555) from the textbook.
    • Exercises due on November 15 Friday (submit these on Canvas or in class):
      1. If two sides of a triangle have lengths a and b and the angle between them has measure C, then what is the area of the triangle?
      2. If a triangle's sides have lengths a, b, and c, then what is the area of the triangle? (Express this using only a, b, c, and non-trigonometric operations. You may use the perimeter or semiperimeter as well, if you find it convenient, but then you must state what that is using only a, b, and/or c.)
    • Exercises from the textbook due on November 18 Monday (submit these through MyLab): 8.4.9, 8.4.11, 8.4.13, 8.4.15, 8.4.17, 8.4.19, 8.4.21, 8.4.25, 8.4.27, 8.4.37.
52. Applications of solving triangles:
    • Reading:
      • Section 8.1 Objective 4 (pages 524–529) from the textbook;
      • Section 8.2 Objective 3 (pages 539–541) from the textbook;
      • Section 8.3 Objective 3 (pages 548&549) from the textbook.
    • Exercises due on November 18 Monday (submit these on Canvas or in class):
      1. If you know the horizontal distance to the base of an object and the angle of elevation to the top of the object and you want to find the height of the object, then would you use the sine, the cosine, or the tangent of the angle of elevation?
      2. If a bearing is N30°E, then what is the angle that this direction makes with due north, and what angle does it make with due east?
      3. If you divide a polygon with n sides into triangles, then how many triangles will you need?
    • Exercises from the textbook due on November 19 Tuesday (submit these through MyLab): 8.1.43, 8.1.45, 8.1.47, 8.1.51, 8.1.63, 8.2.39, 8.2.49, 8.3.45, 8.3.57, 8.4.46, 8.4.53.
53. Harmonic motion:
    • Reading: Section 8.5 (pages 559–565) from the textbook.
    • Exercises due on November 19 Tuesday (submit these on Canvas or in class):
      1. Fill in the blank with more than one word: If the position of an object is a sinusoidal function of time, then the object is undergoing _________ motion.
      2. If the sinusoidal function is modified so that the amplitude is an exponential function with a negative growth rate (instead of a constant), then the object is undergoing _________ motion.
    • Exercises from the textbook due on November 20 Wednesday (submit these through MyLab): 8.5.7, 8.5.9, 8.5.11, 8.5.13, 8.5.15, 8.5.17, 8.5.19, 8.5.21, 8.5.23, 8.5.25, 7.3.109.
54. Polar coordinates:
    • Reading: Section 9.1 through Objective 3 (pages 576–582) from the textbook.
    • Exercises due on November 20 Wednesday (submit these on Canvas or in class):
      1. Fill in the blanks with expressions: Given a point with polar coordinates (r, θ), its rectangular coordinates are (x, y) = (___, ___).
      2. True or false: For each point P in the coordinate plane, for each pair (r, θ) of real numbers that gives P in polar coordinates, r ≥ 0 and 0 ≤ θ < 2π.
      3. True or false: For each point P in the coordinate plane, for some pair (r, θ) of real numbers that gives P in polar coordinates, r ≥ 0 and 0 ≤ θ < 2π.
    • Exercises from the textbook due on November 20 Wednesday (submit these through MyLab): 9.1.13–20, 9.1.21, 9.1.23, 9.1.25, 9.1.27, 9.1.31, 9.1.33, 9.1.35, 9.1.45, 9.1.47, 9.1.49, 9.1.51, 9.1.53, 9.1.59, 9.1.63.
55. Graphing in polar coordinates:
    • Reading:
      • The rest of Section 9.1 (pages 582&583) from the textbook;
      • Section 9.2 (pages 585–597) from the textbook.
    • Exercises due on November 21 Thursday (submit these on Canvas or in class):
      1. Let x and y be rectangular coordinates, and let r and θ be the corresponding polar coordinates.
         1. Express the following quantities using only x and y: r² = _____, tan θ = _____.
         2. Express the following quantities using x, y, and/or r: sin θ = _____, cos θ = _____.
      2. Let a be a positive number, and consider the circle given in polar coordinates by r = 2a sin θ. The radius of this circle is ___, and its centre is (___, ___) in rectangular coordinates.
      3. Let n be a positive integer, and consider the rose curve given in polar coordinates by r = sin(nθ). If n is even, then this rose has ___ petals; if n is odd, then it has ___ petals.
    • Exercises from the textbook due on November 22 Friday (submit these through MyLab): 9.1.77, 9.1.79, 9.1.83, 9.1.85, 9.2.15, 9.2.17, 9.2.19, 9.2.21, 9.2.23, 9.2.31–38, 9.2.39, 9.2.43, 9.2.47, 9.2.51, 9.2.55, 9.2.59.
56. Complex numbers:
    • Reading:
      • Section 9.3 (pages 600–607) from the textbook;
      • My handout on complex numbers (DjVu).
    • Exercises due on November 22 Friday (submit these on Canvas or in class):
      1. What is the magnitude (absolute value) of the complex number x + iy?
      2. Write the complex number with magnitude r and argument θ.
      3. What is the product of r₁(cos θ₁ + i sin θ₁) and r₂(cos θ₂ + i sin θ₂)?
    • Exercises from the textbook due on November 25 Monday (submit these through MyLab): 9.3.13, 9.3.15, 9.3.17, 9.3.19, 9.3.21, 9.3.23, 9.3.25, 9.3.29, 9.3.33, 9.3.35, 9.3.37, 9.3.41, 9.3.43, 9.3.45, 9.3.47, 9.3.49, 9.3.53, 9.3.55, 9.3.57, 9.3.59, 9.3.61, 9.3.63.
57. Vectors:
    • Reading: Section 9.4 (pages 609–619) from the textbook.
    • Exercises due on November 22 Friday (submit these on Canvas or in class):
      1. Give a formula for the vector from the initial point (x₁, y₁) to the terminal point (x₂, y₂).
      2. Give a formula for the magnitude (or norm, or length) of the vector ⟨a, b⟩.
    • Exercises from the textbook due on November 25 Monday (submit these through MyLab): 9.4.11, 9.4.13, 9.4.15, 9.4.17, 9.4.27, 9.4.29, 9.4.37, 9.4.39, 9.4.43, 9.4.45, 9.4.49, 9.4.51.
58. Vectors and angles:
    • Reading: Section 9.5 (pages 624–629) from the textbook.
    • Exercises due on November 25 Monday (submit these on Canvas or in class):
      1. State a formula for the dot product u ⋅ v of two vectors using only their lengths |u| and |v|, the angle θ = ∠(u, v) between them, and real-number operations.
      2. State a formula for the dot product of ⟨a, b⟩ and ⟨c, d⟩ using only real-number operations and the rectangular components a, b, c, and d.
    • Exercises from the textbook due on November 26 Tuesday (submit these through MyLab): 9.4.61, 9.4.63, 9.4.65, 9.4.67, 9.4.69, 9.5.9, 9.5.11, 9.5.13, 9.5.15, 9.5.17, 9.5.19, 9.5.21, 9.5.23, 9.5.25.

Quizzes

1. Graphs and functions:
   • Review date: September 6 Friday.
   • Date due: September 9 Monday.
   • Corresponding problem sets: 1–9.
   • Help allowed: Your notes, a self-contained calculator.
   • NOT allowed: The textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #9 and #11.
2. Operations on functions:
   • Review date: September 20 Friday.
   • Date due: September 23 Monday.
   • Corresponding problem sets: 10–18.
   • Help allowed: Your notes, a self-contained calculator.
   • NOT allowed: The textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #2, #6, and #9.
3. Rational and logarithmic functions:
   • Review date: October 11 Friday.
   • Date due: October 16 Wednesday.
   • Corresponding problem sets: 19–28.
   • Help allowed: Your notes, a self-contained calculator.
   • NOT allowed: The textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #1 and #6.
4. Trigonometric functions:
   • Review date: October 25 Friday.
   • Date due: October 28 Monday.
   • Corresponding problem sets: 29–37.
   • Help allowed: Your notes, a self-contained calculator.
   • NOT allowed: The textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #1, #2, #8, and #9.
5. Analytic trigonometry:
   • Review date: November 8 Friday.
   • Date due: November 11 Monday.
   • Corresponding problem sets: 38–47.
   • Help allowed: Your notes, a self-contained calculator.
   • NOT allowed: The textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #1 and #2.
6. Applications of trigonometry:
   • Review date: November 26 Tuesday.
   • Date due: December 2 Monday.
   • Corresponding problem sets: 48–57.
   • Help allowed: Your notes, a self-contained calculator.
   • NOT allowed: The textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #7.

Final exam

For the exam, you may use one sheet of notes that you wrote yourself; please take a scan or a picture of this (both sides) and submit it on Canvas. However, you may not use your book or anything else not written by you. You certainly should not talk to other people! Calculators are allowed (although you shouldn't really need one), but not communication devices (like cell phones).

The exam consists of questions similar in style and content to those in the practice exam (DjVu).

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