Trigonometry Question

Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 1 of 17 Course Name: Precalculus: Trigonometry Course ID: MTHH044060 Student: Anderson Sandquist Student ID: B78874517 Generated Date: June 20, 2024 Test Version: R Test Progress Test 2 Progress Test 2 (Evaluation 52) covers the course materials that were assigned in Units 3 and 4. Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. You may not have access to notes or any of the course materials while you are taking the test. You may also use your graphing calculator on this test. The Summary of Formulas and Trigonometric Tables from the Appendix is included for your use during the test. Use this link to access supplemental information that you may use as you take this Progress Test. ____ 1. Reduce to a single function of one angle. A. tan 32° 30′ B. tan 130° C. cot 32° 30′ D. cot 130° ____ 2. What is the variation of this function? y = cos θ; to π A. Increases from 0 to 1. B. Increases through all negative values to 0. C. Decreases through all positive values to 1. D. Decreases from 0 to −1. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 1 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 2 of 17 ____ 3. Given , which is in quadrant II, find sec θ. A. B. –2 C. D. ____ 4. Give the extreme values of the function . A. 1 and −1 B. C. −5 and 5 D. ____ 5. Find the inverse of f = {(4, 1), (3, 7), (2, 8), (6, 3)} A. {(4, 3), (2, 6), (1, 7), (8, 3)} B. {(4, 1), (3, 7), (2, 8), (6, 3)} C. {(1, 4), (7, 3), (8, 2), (3, 6)} D. {(3, 4), (6, 2), (7, 1), (3, 8)} Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 2 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 3 of 17 ____ 6. Construct one period of the graph of the equation . Start at x = 0. A. B. C. D. ____ 7. Given , which is in quadrant II, find cos θ. A. B. C. D. ____ 8. Evaluate the expression . A. B. C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 3 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 4 of 17 ____ 9. Given , which is in quadrant II, find sin θ. A. B. C. D. ____ 10. Evaluate the expression: A. B. C. D. ____ 11. Find the inverse of . A. B. y = x C. y = 1 D. x = 1 ____ 12. Evaluate the expression cos (cos–1 ). A. 1 B. C. D. 0 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 4 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 5 of 17 ____ 13. Evaluate the expression: . A. B. C. −2 D. ____ 14. The period of the graph of is A. B. 2 π C. π D. ____ 15. Evaluate the expression: Cos–1 (1) A. 0 B. 1 C. −1 D. ____ 16. Given: , for A and B in quadrant III. Find the values of the following: tan (A – B) A. B. C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 5 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 6 of 17 ____ 17. Evaluate the expression . A. B. C. D. ____ 18. What is the period of the graph of y = cot x? A. B. π C. D. 2π ____ 19. Given , which is in quadrant I, find cot θ. A. B. C. D. ____ 20. What is the period of the graph of y = 3 sin 2x ? A. 4π B. π C. D. 2π Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 6 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 7 of 17 ____ 21. Given , which is in quadrant I, find csc θ. A. B. C. D. ____ 22. What is the best identity you could use to convert the RHS: csc θ cos θ to cot θ? A. B. C. D. ____ 23. Evaluate cos 69° cos 24° + sin 69° sin 24°. What is the value? A. B. 0.0523 C. 0.9986 D. ____ 24. Express the product of 2cos3θcosθ as an algebraic sum. A. cos (3θ – θ) + cos (3θ + θ) B. cos (3θ + θ) + sin (3θ – θ) C. cos (3θ + θ) + cos (3θ – θ) D. cos (3θ + θ) – cos (3θ – θ) Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 7 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 8 of 17 ____ 25. Construct one period of the graph of the equation y = sec x. Start at x = 0. A. B. C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 8 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 9 of 17 ____ 26. Find the solution set of each equation in the interval: 0 ≤ x < 2π. sec x = 3 – 2 cos x A. B. C. D. ____ 27. Find the exact value of cos (–15°). A. B. C. D. ____ 28. Find the amplitude of the equation: y = 4sin4x. A. 4 B. 16 C. 2 D. 1 ____ 29. Evaluate 2 sin 67.5° cos 67.5°. What is the second step equal to? A. sin 2(67.5°) B. C. cos 2 (67.5°) D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 9 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 10 of 17 ____ 30. What is one identity you could use to convert the LHS: csc θ cos θ to cot θ? A. B. C. D. ____ 31. Construct one period of the graph of the equation . Start at x = 0. A. B. C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 10 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 11 of 17 ____ 32. Given: , for A and B in quadrant III. Find the values of the following: A. B. C. D. ____ 33. Find the exact value of sin (75°). A. B. C. D. ____ 34. What are the extreme values of ? A. 2 and –2 B. 1 and –1 C. 4 and –4 D. ____ 35. Evaluate . What is the value? A. 0.2493 B. 4.011 C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 11 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 12 of 17 ____ 36. What is the phase shift of A. to the right B. to the left C. to the left D. to the right ____ 37. Given: ? , angle A is in Quadrant III and angle B is in Quadrant I. Find the values of the following: sin (A + B) = A. B. C. D. ____ 38. Between what values of x is cos x an increasing function? A. Between x = 2n π and (2n + 1)π, where n is any integer. B. Between x = (2n – 1)π and 2n π, where n is any integer. C. Between x = (2n – 1)π and 1n π, where n is any integer. D. Between x = 2n π and 2n, where n is any integer. ____ 39. Find the solution set of each equation in the interval: 0 ≤ x < 2π. A. B. { π } C. { 2 π } D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 12 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 13 of 17 ____ 40. Evaluate sin 54° cos 9° – cos 54° sin 9°. What is the second step equal to? A. sin (54° – 9°) B. sin (54° + 9°) C. cos (54° + 9°) D. cos (54° – 9°) ____ 41. Give the size and direction of the phase shift of the second equation relative to the first equation. A. to the left B. to the right C. to the left D. to the right ____ 42. Find the solution set of 0 ≤ x < 2π in the interval 2 cos x + tan x – sec x = 0. A. B. {0, π} C. D. 0 ____ 43. Find the solution set of each equation in the interval: 0 ≤ x < 2π. sec x – 2 = 0 A. B. C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 13 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 14 of 17 ____ 44. Express the following as a function of twice the given angle: cos x = A. B. C. D. ____ 45. Express the following algebraic sum as a product: sin28° + sin32° A. 2cos28°cos32° B. 2sin30°cos2° C. 2sin60°cos4° D. cos30°cos2° ____ 46. Given: , for A and B in quadrant III. Find the values of the following: tan 2A A. B. C. D. ____ 47. Reduce each of the following expressions to a single function of one angle: cos (45° – A) + cos (45° + A) A. B. C. D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 14 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 15 of 17 ____ 48. Find the solution set of each equation in the interval: 0 ≤ x < 2π. 4 cos2x = 2 A. B. C. D. ____ 49. What are the extreme values of ? A. 1 and – 1 B. π and –π C. 4 and −4 D. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 15 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 16 of 17 ____ 50. Graph the inverse of the following: A. B. C. D. Carefully review your answers on this progress test and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the online test submission page in the presence of your proctor. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 16 of 17 Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 17 of 17 The University of Nebraska is an equal opportunity educator and employer. ©2024, The Board of Regents of the University of Nebraska. All rights reserved. Progress Test 2 – MTHH044060 – Anderson Sandquist – Jun 20, 2024 – Page 17 of 17

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