MATH-1200-ES31

Course administration:

• Canvas page (where you must log in).
• Help with DjVu (if you have trouble reading the files on this page).
• Course policies (TBA).
• Class hours: Mondays, Wednesdays, and Fridays from 10:00 to 10:50 in ESQ 100D.
• Class Zoom meeting: 928-6157-2182.
• Final exam time: December 11 Friday from 10:00 to 11:40 in ESQ 100D.

• Name: Toby Bartels, PhD.
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Virtual office hours:
  • Mondays and Wednesdays from 1:00 PM to 2:00,
  • Tuesdays and Thursdays from 10:30 to 12:00, and
  • by appointment.

Readings

Basic trigonometry

1. General review:
   • Reading from the textbook: Section 2.1 (pages 150–153).
   • Exercises due on August 26 Wednesday:
     1. In which number quadrant are both coordinates positive?
     2. Write down a formula for the distance between the points (x₁, y₁) and (x₂, y₂) in a rectangular coordinate system.
     3. If the two short sides of a right triangle have lengths 3 and 4, then what is the length of the hypotenuse?
   • Exercises from the textbook due on August 28 Friday: 2.1.19, 2.1.21, 2.1.23, 2.1.25, 2.1.27, 2.1.31, 2.1.39, 2.1.41, 2.1.43.
2. Circles:
   • Reading from the textbook: Section 2.4 (pages 185–188).
   • Exercises due on August 28 Friday:
     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 August 31 Monday: 2.4.5, 2.4.9, 2.4.11, 2.4.13, 2.4.15, 2.4.17, 2.4.21, 2.4.23, 2.4.25, 2.4.27.
3. Angles:
   • Reading from the textbook: Section 7.1 through Objective 4 (pages 518–524).
   • Exercises due on August 31 Monday:
     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 September 2 Wednesday: 7.1.11, 7.1.13, 7.1.15, 7.1.17, 7.1.19, 7.1.21, 7.1.23, 7.1.26, 7.1.35, 7.1.37.
4. Length and area with radians:
   • Reading from the textbook: The rest of Section 7.1 (pages 524–526).
   • Exercises due on September 2 Wednesday: 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 September 4 Friday: 7.1.71, 7.1.73, 7.1.79, 7.1.81, 7.1.87, 7.1.91, 7.1.95, 7.1.99.
5. Right triangles:
   • Reading from the textbook: Section 7.2 (pages 531–538).
   • Exercises due on September 4 Friday:
     1. Fill in the blank: The sine of the complement of θ is the _____ of θ.
     2. If θ is the measure of an acute angle in a right triangle, then what is the cotangent of θ as a ratio of the lengths of the adjacent leg, the opposite leg, and/or the hypotenuse?
     3. If the secant of an angle is 3, then what is its cosine?
   • Exercises from the textbook due on September 9 Wednesday: 7.2.9, 7.2.10, 7.2.11, 7.2.12, 7.2.13, 7.2.15, 7.2.17, 7.2.23, 7.2.27, 7.2.31, 7.2.33, 7.2.37, 7.2.39, 7.2.41, 7.2.43, 7.2.45, 7.2.57, 7.2.65.
6. Special angles:
   • Reading from the textbook: Section 7.3 through Objective 2 (pages 543–546).
   • Exercise due on September 9 Wednesday: Write down the exact values of the sine, cosine, tangent, cotangent, secant, and cosecant of π/6 (or 30°), π/4 (or 45°), and π/3 (or 60°). (This is 18 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.)
   • Exercises from the textbook due on September 11 Friday: 7.3.7, 7.3.19, 7.3.21, 7.3.23, 7.3.27, 7.3.29.
7. Applications with acute angles:
   • Reading from the textbook: The rest of Section 7.3 (pages 546–549).
   • Exercises due on September 11 Friday:
     1. 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?
     2. 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?
   • Exercises from the textbook due on September 14 Monday: 7.3.31, 7.3.33, 7.3.35, 7.3.59, 7.3.69, 7.3.73, 7.3.79.
8. General angles:
   • Reading from the textbook: Section 7.4 through Objective 5 (pages 555–561).
   • Exercises due on September 14 Monday:
     1. Two angles that differ by one or more full turns are called _____ angles.
     2. If the six fundamental trigonometric functions all have the same absolute values at θ as at α and α is an acute angle, then α is the _____ angle of θ.
     3. Which of the six fundamental trigonometric functions of θ are positive when θ terminates in Quadrant III?
   • Exercises from the textbook due on September 16 Wednesday: 7.4.11, 7.4.15, 7.4.17, 7.4.21, 7.4.31, 7.4.33, 7.4.39, 7.4.51, 7.4.53, 7.4.57, 7.4.59, 7.4.61, 7.4.75.
9. Circular trigonometry:
   • Reading from the textbook:
     • The rest of Section 7.4 (page 562);
     • Section 7.5 through "Trigonometric Functions of Angles" (pages 566–570).
   • Exercises due on September 16 Wednesday:
     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 (a, b), express sin t, cos t, tan t, cot t, sec t, and csc t using only a and b.
     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.
   • Exercises from the textbook due on September 18 Friday: 7.4.83, 7.4.87, 7.4.93, 7.5.11, 7.5.13, 7.5.17, 7.5.19, 7.5.23, 7.5.31, 7.5.33, 7.5.39, 7.5.41, 7.5.47, 7.5.49.
10. The trigonometric functions:
    • Reading from the textbook: The rest of Section 7.5 (pages 570–575).
    • Exercises due on September 18 Friday:
      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 September 21 Monday: 7.5.63, 7.5.65, 7.5.69, 7.5.81, 7.5.85, 7.5.87, 7.6.3.

Advanced trigonometry

11. Basic sinusoidal graphs:
    • Reading from the textbook:
      • Section 7.6 through the box before Example 1 (pages 579&580);
      • Section 7.6 Objective 2 through the box before Example 3 (pages 581&582).
    • Exercises due on September 21 Monday: Each of these questions has infinitely many answers; either list enough that the pattern is clear in both directions, or use a formula involving an arbitrary integer k.
      1. What are the intercepts of the graph of the sine function?
      2. What are the turning points (local max and min) of the graph of the sine function?
      3. What are the intercepts of the graph of the cosine function? (Be careful not to miss one!)
      4. What are the turning points of the graph of the cosine function?
    • Exercises from the textbook due on September 23 Wednesday: 7.6.6, 7.6.8, 7.6.11, 7.6.13.
12. More basic graphs:
    • Reading from the textbook:
      • Section 7.7 through "The Graph of the Cotangent Function y = cot x" (pages 594–596);
      • Section 7.7 Objective 3 (pages 597&598).
    • Exercises due on September 23 Wednesday:
      1. What are the intercepts of the graph of the tangent function?
      2. What are the intercepts of the graph of the cotangent function?
      3. What are the linear asymptotes to the graphs of the tangent and secant functions?
      4. What are the linear asymptotes to the graphs of the cotangent and cosecant functions?
    • Exercises from the textbook due on September 25 Friday: 7.7.3, 7.7.6, 7.7.7, 7.7.10, 7.7.11, 7.7.12, 7.7.13, 7.7.16.
13. Coordinate transformations:
    • Review from (mostly) the textbook:
      • Section 3.5 (pages 254–263);
      • My online notes on linear coordinate transformations.
    • Exercises due on September 28 Monday: 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 30 Wednesday: 3.5.5, 3.5.6, 3.5.19, 3.5.21, 3.5.23, 3.5.25, 3.5.29, 3.5.30, 3.5.33, 3.5.35, 3.5.53, 3.5.41, 3.5.45, 3.5.61.
14. Transformations of trigonometric functions:
    • Reading from the textbook:
      • Section 7.6 Objective 1 Examples 1&2 (pages 580&581);
      • Section 7.6 Objective 2 Example 3 (page 582);
      • Section 7.7 Objective 2 (pages 596&597);
      • Section 7.7 Objective 4 (pages 598&599).
    • Exercises due on September 30 Wednesday: 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 (as a function of 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 2 Friday: 7.6.23–32, 7.7.17, 7.7.21, 7.7.23, 7.7.25, 7.7.29, 7.7.31.
15. Sinusoidal functions:
    • Reading from (mostly) the textbook:
      • My handout on sinusoidal functions (DjVu);
      • The rest of Section 7.6 (pages 582–588);
      • Section 7.8 Objective 1 (pages 601–605).
    • Exercises due October 2 Friday:
      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 0 ≤ φ < 2π, then what is the phase shift of f?
    • Exercises from the textbook due on on October 5 Monday: 7.6.35, 7.6.39, 7.6.51, 7.6.57, 7.6.61, 7.6.87, 7.8.9, 7.8.11, 7.8.19, 7.8.17.
16. Inverse trigonometric operations:
    • Reading from the textbook:
      • Section 8.1 through Objective 7 (pages 622–630);
      • Section 8.2 through Objective 2 (pages 653–637).
    • Exercises due on October 5 Monday: 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 7 Wednesday: 8.1.19, 8.1.21, 8.2.11, 8.2.13, 8.2.19, 8.1.39, 8.1.41, 8.1.43, 8.1.45, 8.1.51, 8.1.53, 8.1.55, 8.1.57.
17. More inverse trigonometric operations:
    • Reading from (mostly) the textbook:
      • The rest of Section 8.1 (pages 630&631).
      • The rest of Section 8.2 (pages 637&638);
      • My handout on inverse trigonometric operations (DjVu).
    • Exercises due on October 7 Wednesday:
      1. cos sin⁻¹ x = ___ (if either side exists).
      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 9 Friday: 8.2.33, 8.2.35, 8.2.47, 8.2.49, 8.1.59, 8.1.61, 8.2.61, 8.2.63, 8.2.65.
18. Sum-angle formulas:
    • Reading from the textbook: Section 8.5 Objectives 1–3 (pages 659–666).
    • Exercises due on October 9 Friday: 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. cos(α − β) = ___.
    • Exercises from the textbook due on October 12 Monday: 8.5.15, 8.5.17, 8.5.19, 8.5.21, 8.5.35, 8.5.37, 8.5.39, 8.5.41, 8.5.77.
19. Double-angle and related formulas:
    • Reading from the textbook:
      • Section 8.6 through Example 3 in Objective 2 (pages 672&675);
      • Section 8.7 (pages 683–685).
    • Exercises due on October 12 Monday:
      1. Express sin(2α) using sin α and/or cos α.
      2. Express sin² α using sin(2α) and/or cos(2α).
      3. Express sin α sin β using sin(α + β), sin(α − β), cos(α + β), and/or cos(α − β).
      4. Factor sin α + sin β so that each factor has at most one trigonometric operation.
    • Exercises from the textbook due on October 14 Wednesday: 8.6.83, 8.6.85, 8.6.87, 8.7.7, 8.7.9, 8.7.11, 8.7.13, 8.7.15, 8.7.17, 8.7.19, 8.7.21, 8.7.23.
20. Half-angle formulas:
    • Reading from the textbook: Section 8.6 Objective 3 (pages 676–678).
    • Exercises due on October 14 Wednesday: 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 October 16 Friday: 8.6.25, 8.6.29, 8.6.23, 8.6.27, 8.6.9, 8.6.11, 8.6.13, 8.6.15, 8.6.17, 8.6.19.
21. Simplifying trigonometric expressions:
    • Reading from (mostly) the textbook:
      • My handout on simplifying trigonometric expressions (DjVu);
      • Section 8.4 (pages 651–656).
    • Exercises due on October 16 Friday:
      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?
    • Exercises from the textbook due on October 21 Wednesday: 8.4.1, 8.4.2, 8.4.6, 8.4.8, 8.4.11, 8.4.15, 8.4.17, 8.4.29, 8.4.55, 8.4.71, 8.4.95.
22. Trigonometric equations:
    • Reading from the textbook: Section 8.3 (pages 641–646).
    • Exercises due on October 21 Wednesday:
      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 October 23 Friday: 8.3.13, 8.3.23, 8.3.25, 8.3.27, 8.3.37, 8.3.39, 8.3.109, 8.3.115.
23. Tricky trigonometric equations:
    • Reading from the textbook:
      • Section 8.5 Objective 4 (pages 666–668);
      • Section 8.6 Objective 2 Examples 4&5 (pages 675&676).
    • Exercises due on October 23 Friday:
      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 October 26 Monday: 8.3.61, 8.3.73, 8.5.93, 8.5.97, 8.6.75, 8.6.77, 8.7.47.

Applications

24. Solving right triangles:
    • Reading from the textbook: Section 9.1 (pages 694–696).
    • Exercises due on October 26 Monday:
      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 October 28 Wednesday: 9.1.4, 9.1.11, 9.1.13, 9.1.15, 9.1.17, 9.1.19, 9.1.21, 9.1.23, 9.1.37.
25. The Law of Sines:
    • Reading from the textbook: Section 9.2 through Objective 2 (pages 700–704).
    • Exercises due on October 28 Wednesday: 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 October 30 Friday: 9.2.9, 9.2.11, 9.2.13, 9.2.15, 9.2.18, 9.2.27, 9.2.29, 9.2.33, 9.2.35, 9.2.37.
26. The Law of Cosines:
    • Reading from (mostly) the textbook:
      • Section 9.3 through Objective 2 (pages 711–713);
      • My handout on solving triangles (DjVu).
    • Exercises due on November 2 Monday:
      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 4 Wednesday: 9.3.9, 9.3.11, 9.3.13, 9.3.15.
27. Area of triangles:
    • Reading from the textbook: Section 9.4 (pages 718–720).
    • Exercises due on November 4 Wednesday:
      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 it is using only a, b, and c.)
    • Exercises from the textbook due on November 6 Friday: 9.4.9, 9.4.11, 9.4.13, 9.4.15, 9.4.17, 9.4.19, 9.4.21, 9.4.25, 9.4.27, 9.4.37.
28. Applications of solving triangles:
    • Reading from the textbook:
      • Section 9.2 Objective 3 (pages 704–707);
      • Section 9.3 Objective 3 (pages 713&714).
    • Exercises due on November 6 Friday:
      1. 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?
      2. If you divide a polygon with n sides into triangles, how many triangles will you need?
    • Exercises from the textbook due on November 9 Monday: 9.2.39, 9.2.49, 9.3.45, 9.3.57, 9.4.46, 9.4.53.
29. Harmonic motion:
    • Reading from the textbook: Section 9.5 (pages 724–730).
    • Exercises due on November 9 Monday:
      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 11 Wednesday: 9.5.7, 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.
30. Polar coordinates:
    • Reading from the textbook: Section 10.1 through Objective 3 (pages 740–746).
    • Exercises due on November 11 Wednesday:
      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 13 Friday: 10.1.13–20, 10.1.21, 10.1.23, 10.1.25, 10.1.27, 10.1.31, 10.1.33, 10.1.35, 10.1.45, 10.1.47, 10.1.49, 10.1.51, 10.1.53, 10.1.59, 10.1.63.
31. Equations in polar coordinates:
    • Reading from the textbook:
      • Section 10.1 Objective 4 (pages 746&747);
      • Section 10.2 through Objective 1 (pages 749–753).
    • Exercises due on November 13 Friday: Let x and y be rectangular coordinates, and let r and θ be the corresponding polar coordinates.
      • Express the following quantities using only x and y:
        1. r²,
        2. tan θ;
      • Express the following quantities using x, y, and/or r:
        3. sin θ,
        4. cos θ.
    • Exercises from the textbook due on November 16 Monday: 10.1.77, 10.1.79, 10.1.83, 10.1.85, 10.2.15, 10.2.17, 10.2.19, 10.2.21, 10.2.23.
32. Graphing in polar coordinates:
    • Reading from the textbook: The rest of Section 10.2 (pages 753–761).
    • Exercises due on November 16 Monday:
      1. 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.
      2. 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 18 Wednesday: 10.2.31–38, 10.2.39, 10.2.43, 10.2.47, 10.2.51, 10.2.55, 10.2.59.
33. Complex numbers:
    • Reading from the textbook: Section 10.3 (pages 764–771).
    • Exercises due on November 18 Wednesday:
      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 20 Friday: 10.3.13, 10.3.15, 10.3.17, 10.3.19, 10.3.21, 10.3.23, 10.3.25, 10.3.29, 10.3.33, 10.3.35, 10.3.37, 10.3.41, 10.3.43, 10.3.45, 10.3.47, 10.3.49, 10.3.53, 10.3.55, 10.3.57, 10.3.59, 10.3.61, 10.3.63.
34. Vectors:
    • Reading from the textbook: Section 10.4 (pages 773–783).
    • Exercises due on November 20 Friday:
      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 23 Monday: 10.4.11, 10.4.13, 10.4.15, 10.4.17, 10.4.27, 10.4.29, 10.4.37, 10.4.39, 10.4.43, 10.4.45, 10.4.49, 10.4.51.
35. Vectors and angles:
    • Reading from the textbook: Section 10.5 (pages 788–793).
    • Exercises due on November 23 Monday:
      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 30 Monday: 10.4.61, 10.4.63, 10.4.65, 10.4.67, 10.4.69, 10.5.9, 10.5.11, 10.5.13, 10.5.15, 10.5.17, 10.5.19, 10.5.21, 10.5.23, 10.5.25.

Quizzes

1. Basic trigonometry:
   • Review date: September 25 Friday (in class).
   • Date due on MyLab: September 28 Monday (before class).
   • Corresponding problems sets: 1–10.
   • Help allowed: Your notes, calculator. (If a question tells you not to use a calculator, you may still use the calculator to check, but be sure to give an exact answer.)
   • NOT allowed: 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 #3, #7, and #9. (If a question tells you not to use a calculator, then be sure that your work shows how you can solve the problem without using one.)
2. Advanced trigonometry:
   • Review date: October 30 Friday (in class).
   • Date due on MyLab: November 2 Monday (before class).
   • Corresponding problems sets: 11–23.
   • Help allowed: Your notes, calculator. (In graphing problems, while you may still use a graphing calculator to check, you should be able to solve the problem without one.)
   • NOT allowed: 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 #1. (In graphing problems, be sure that your work shows how you can solve the problem without using a graphing calculator.)
3. Applications:
   • Review date: December 4 Friday (in class).
   • Date due on MyLab: December 7 Monday (before class).
   • Corresponding problems sets: 24–35.
   • Help allowed: Your notes, calculator.
   • NOT allowed: 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 #7, #8, and #11.

Final exam

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