# MATH-1200-WBP81

Welcome to the permanent home page for Section WBP81 of MATH-1200 (Trigonometry) at Southeast Community College in the second half of the Spring term of 2022. I am Toby Bartels, your instructor.

## Contact information

Feel free to send a message at any time, even nights and weekends (although I'll be slower to respond then).

The official textbook for the course is the 11th Edition of Algebra & Trigonometry by Sullivan published by Prentice-Hall (Pearson). You automatically get an online version of this textbook through Canvas, although you can use a print version instead if you like. This comes with access to Pearson MyLab, integrated into Canvas, on which many of the assignments appear.

### Basic trigonometry

1. General review:
• Reading from the textbook: Section 2.1 (pages 150–153).
• Exercises due on March 21 Monday (submit these on Canvas):
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 March 22 Tuesday (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.1.11, O.1.12, 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 March 22 Tuesday (submit these on Canvas):
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 March 23 Wednesday (submit these through MyLab): 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 March 23 Wednesday (submit these on Canvas):
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 March 24 Thursday (submit these through MyLab): 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 March 24 Thursday (submit these on Canvas): 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 March 25 Friday (submit these through MyLab): 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 March 25 Friday (submit these on Canvas):
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 March 26 Saturday (submit these through MyLab): 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 March 27 Sunday (submit this on Canvas): 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 March 28 Monday (submit these through MyLab): 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 March 28 Monday (submit these on Canvas):
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 March 29 Tuesday (submit these through MyLab): 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 March 29 Tuesday (submit these on Canvas):
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 March 30 Wednesday (submit these through MyLab): 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:
• The rest of Section 7.4 (page 562);
• Section 7.5 through "Trigonometric Functions of Angles" (pages 566–570).
• Exercises due on March 30 Wednesday (submit these on Canvas):
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 March 31 Thursday (submit these through MyLab): 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 March 31 Thursday (submit these on Canvas):
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 April 1 Friday (submit these through MyLab): 7.5.63, 7.5.65, 7.5.69, 7.5.81, 7.5.85, 7.5.87, 7.6.3.
Quiz 1, covering the material in Problem Sets 1–10, is available on April 1 Friday and due on April 4 Monday.

1. Basic sinusoidal graphs:
• 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 April 1 Friday (submit these on Canvas): 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 April 2 Saturday (submit these through MyLab): 7.6.6, 7.6.8, 7.6.11, 7.6.13.
2. More basic graphs:
• 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 April 4 Monday (submit these on Canvas):
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 April 5 Tuesday (submit these through MyLab): 7.7.3, 7.7.6, 7.7.7, 7.7.10, 7.7.11, 7.7.12, 7.7.13, 7.7.16.
3. Coordinate transformations:
• Review from (mostly) the textbook:
• Exercises due on April 5 Tuesday (submit these on Canvas): 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 April 6 Wednesday (submit these through MyLab): 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.
4. Transformations of trigonometric functions:
• 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 April 6 Wednesday (submit these on Canvas): 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 April 7 Thursday (submit these through MyLab): 7.6.23–32, 7.7.17, 7.7.21, 7.7.23, 7.7.25, 7.7.29, 7.7.31.
5. Sinusoidal functions:
• Reading from (mostly) the textbook:
• Exercises due on April 7 Thursday (submit these on Canvas):
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 April 8 Friday (submit these through MyLab): 7.6.35, 7.6.39, 7.6.51, 7.6.57, 7.6.61, 7.6.87.
6. Inverse trigonometric operations:
• Section 8.1 through Objective 7 (pages 622–630);
• Section 8.2 through Objective 2 (pages 653–637).
• Exercises due on April 8 Friday (submit these on Canvas): Fill in all of these blanks with algebraic expressions (or constants). Work only in the real number system.
1. That y = sin−1x means that x = ___ and ___ ≤ y ≤ ___.
2. cos−1x exists if and only if ___ ≤ x ≤ ___.
3. cos−1 cos θ = θ if and only if ___ ≤ θ ≤ ___.
• Exercises from the textbook due on April 9 Saturday (submit these through MyLab): 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.
7. More inverse trigonometric operations:
• Reading from (mostly) the textbook:
• Exercises due on April 10 Sunday (submit these on Canvas):
1. cos sin−1x = ___ (if either side exists).
2. If f is the function given by f(x) = sin−1x, 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 April 11 Monday (submit these through MyLab): 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.
8. Sum-angle formulas:
• Section 8.5 Objectives 1–3 (pages 659–666);
• Section 8.6 through Example 3 in Objective 2 (pages 672&675).
• Exercises due on April 11 Monday (submit these on Canvas): 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 April 12 Tuesday (submit these through MyLab): 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, 8.6.83, 8.6.85, 8.6.87.
9. Half-angle formulas:
• Reading from the textbook: Section 8.6 Objective 3 (pages 676–678).
• Exercises due on April 12 Tuesday (submit these on Canvas): 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 April 13 Wednesday (submit these through MyLab): 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.
10. Simplifying trigonometric expressions:
• Reading from (mostly) the textbook:
• Exercises due on April 13 Wednesday (submit these on Canvas):
1. Fill in the blank with an expression in which sin θ is the only trigonometric quantity: cos2θ = ___.
2. Factor without using any trigonometric identities: sin2θ − 1 = (___)(___).
3. If you regard a cosine as a square root, then what expression is conjugate to 1 − cos θ? (If you were to multiply the two expressions together, then cos θ should appear only as cos2θ.)
• Exercises from the textbook due on April 14 Thursday (submit these through MyLab): 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.
11. Trigonometric equations:
• Reading from the textbook: Section 8.3 (pages 641–646).
• Exercises due on April 14 Thursday (submit these on Canvas):
1. Write a general form for the solutions of tan x = b using tan−1b 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 April 15 Friday (submit these through MyLab): 8.3.13, 8.3.23, 8.3.25, 8.3.27, 8.3.37, 8.3.39, 8.3.109, 8.3.115.
12. Tricky trigonometric equations:
• Section 8.5 Objective 4 (pages 666–668);
• Section 8.6 Objective 2 Examples 4&5 (pages 675&676).
• Exercises due on April 15 Friday (submit these on Canvas):
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?
• Exercises from the textbook due on April 16 Saturday (submit these through MyLab): 8.3.61, 8.3.73, 8.5.93, 8.5.97, 8.6.75, 8.6.77.
Quiz 2, covering the material in Problem Sets 11–22, is available on April 15 Friday and due on April 18 Monday.

### Applications

1. Solving right triangles:
• Reading from the textbook: Section 9.1 (pages 694–696).
• Exercises due on April 18 Monday (submit these on Canvas):
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 April 19 Tuesday (submit these through MyLab): 9.1.4, 9.1.11, 9.1.13, 9.1.15, 9.1.17, 9.1.19, 9.1.21, 9.1.23.
2. The Law of Sines:
• Reading from the textbook: Section 9.2 through Objective 2 (pages 700–704).
• Exercises due on April 19 Tuesday (submit these on Canvas): 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 April 20 Wednesday (submit these through MyLab): 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.
3. 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 April 20 Wednesday (submit these on Canvas):
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 April 21 Thursday (submit these through MyLab): 9.3.9, 9.3.11, 9.3.13, 9.3.15.
4. Area of triangles:
• Reading from the textbook: Section 9.4 (pages 718–720).
• Exercises due on April 21 Thursday (submit these on Canvas):
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 April 22 Friday (submit these through MyLab): 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.
5. Applications of solving triangles:
• Section 9.2 Objective 3 (pages 704–707);
• Section 9.3 Objective 3 (pages 713&714).
• Exercises due on April 22 Friday (submit these on Canvas):
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 April 23 Saturday (submit these through MyLab): 9.1.37, 9.2.39, 9.2.49, 9.3.45, 9.3.57, 9.4.46, 9.4.53.
6. Polar coordinates:
• Reading from the textbook: Section 10.1 through Objective 3 (pages 740–746).
• Exercises due on April 24 Sunday (submit these on Canvas):
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 April 25 Monday (submit these through MyLab): 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.
7. Equations in polar coordinates:
• Section 10.1 Objective 4 (pages 746&747);
• Section 10.2 through Objective 1 (pages 749–753).
• Exercises due on April 25 Monday (submit these on Canvas): 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:
1. sin θ,
2. cos θ.
• Exercises from the textbook due on April 26 Tuesday (submit these through MyLab): 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.
8. Graphing in polar coordinates:
• Reading from the textbook: The rest of Section 10.2 (pages 753–761).
• Exercises due on April 26 Tuesday (submit these on Canvas):
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 April 27 Wednesday (submit these through MyLab): 10.2.31–38, 10.2.39, 10.2.43, 10.2.47, 10.2.51, 10.2.55, 10.2.59.
9. Vectors:
• Reading from the textbook: Section 10.4 (pages 773–783).
• Exercises due on April 27 Wednesday (submit these on Canvas):
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 April 28 Thursday (submit these through MyLab): 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.
10. Vectors and angles:
• Reading from the textbook: Section 10.5 (pages 788–793).
• Exercises due on April 28 Thursday (submit these on Canvas):
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 April 29 Friday (submit these through MyLab): 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.
Quiz 3, covering the material in Problem Sets 23–32, is available on April 29 Friday and due on May 2 Monday.

## Quizzes

1. Basic trigonometry:
• Date available: April 1 Friday.
• Date due on MyLab: April 4 Monday.
• 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.)
• Date available: April 15 Friday.
• Date due on MyLab: April 18 Monday.
• Corresponding problems sets: 11–22.
• 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:
• Date available: April 29 Friday.
• Date due on MyLab: May 2 Monday.
• Corresponding problems sets: 23–32.
• 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 and #10.

## Final exam

There will be a comprehensive final exam at the end of the term. (You'll arrange to take it sometime from April 29 to May 5.) To speed up grading at the end of the term, the exam will be multiple choice, with no partial credit.

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 will consist of questions similar in style and content to those in the practice final exam (DjVu). The practice final exam counts as a problem set, so be sure to attempt it and let me know how you did.

The final exam will be proctored. If you have access to a computer with a webcam, then you can schedule a time with me to take the exam in a Zoom meeting. If you're near Lincoln, then we can schedule a time for you to take the exam in person. You can also take it in the Testing Center on the main Lincoln campus or in Beatrice or Milford. If none of these will work for you, then contact me as soon as possible to make alternate arrangements. When it's scheduled, you can take the exam on Canvas.

This web page and the files linked from it (except for the official syllabus) were written by Toby Bartels, last edited on 2022 May 2. Toby reserves no legal rights to them.

The permanent URI of this web page is `http://tobybartels.name/MATH-1200/2022SP2/`.