Multiple choice test in trigonometry with answers

Course Name: Precalculus: Trigonometry Student: Aryash Chauhan Course ID: MTHH044059 ID: F68560331 Submittal: 52 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. ____ 1. Express a. as a function of twice the given angle. sin 2 b. ____ 2. c. sin 4 d. sin Express the product of 2sin15°cos65° as an algebraic sum. a. b. c. d. ____ 3. sin(15° + 65°) + sin(15° − 65°) sin(15° − 65°) + sin(15° + 65°) sin(15° + 65°) + cos(15° + 65°) sin(15° − 65°) + cos(15° − 65°) Given: , angle A is in Quadrant I and angle B is in Quadrant II. Find the values of the following: cos (A – B) a. b. c. d. ____ 4. Find the amplitude of the equation: a. b. c. d. 4 16 2 1 . ____ 5. Express the algebraic sum of cos35° + cos15° as a product. a. b. c. d. ____ 6. 2cos25°cos20° 2cos25°cos10° 2cos10°cos50° 2cos50°cos20° What is the period of the graph of y = sin (x + a. 2 b. – )? c. d. ____ 7. Evaluate sin 54° cos 9° – cos 54° sin 9°. What is the second step equal to? a. b. c. d. ____ 8. Which function always increases between its asymptotic values? a. b. c. d. ____ 9. sin (54° – 9°) sin (54° + 9°) cos (54° + 9°) cos (54° – 9°) sine cosine tangent cotangent What is the period of the graph of y = sec x? a. 2 b. 4 c. 3 d. ____ 10. Evaluate the expression a. b. 1 c. d. 0 . ____ 11. Given: tan A = , and cos B = , for A and B in quadrant III. Find the values of the following: a. b. c. d. ____ 12. Graph the inverse of the following: a. b. c. . d. ____ 13. Find the inverse of g = {(3, 1), (2, 6), (5, 7), (4, 7)} a. b. c. d. {(1, 6), (5, 4), (3, 2), (7, 7)} {(6, 1), (4, 5), (2, 3), (7, 7)} {(3, 1), (2, 6), (5, 7), (4, 7)} {(1, 3), (6, 2), (7, 5), (7, 4)} ____ 14. Given , which is in quadrant I, find . a. b. c. d. ____ 15. Give the extreme values of the function a. b. c. d. 2 and −2 1 and −1 . ____ 16. Given , which is in quadrant II, find a. b. c. d. ____ 17. Evaluate the expression: a. b. c. d. . ____ 18. Construct one period of the graph of the equation . Start at x = 0. a. b. c. d. ____ 19. Given a. b. c. d. , which is in quadrant I, find . ____ 20. What is another identity you would use to convert: ? a. b. c. d. ____ 21. Evaluate sin 54° cos 9° – cos 54° sin 9°. What is the value? a. b. c. d. 0.8910 0.4540 ____ 22. Find the solution set of each equation in the interval: 0 ≤ x < 2 . cos2x – sinx = 0 a. { 0, } b. c. d. ____ 23. Find the exact value of cos(195°). a. b. c. d. ____ 24. Construct one period of the graph of the equation y = cot x. Start at x = 0. a. b. c. d. ____ 25. Given , which is in quadrant II, find . a. b. c. −2 d. ____ 26. Evaluate the expression: tan[sin-1(5/13) + cos-1(–3/5)]. a. b. c. d. ____ 27. Evaluate the following expression: a. b. c. d. ____ 28. Find the exact value of sin(75°). a. b. c. d. − ____ 29. Construct one period of the graph of the equation y = cos (x + ). Start at x = 0. a. b. c. d. ____ 30. Give the size and direction of the phase shift of the second equation relative to the first equation. y = cos2x; y = cos(2x + ) a. to the left b. to the right c. to the left d. to the right ____ 31. What is the period of the graph of a. ? 4 b. c. d. 2 ____ 32. Find the solution set of each equation in the interval: 0 ≤ x < 2 . sin x + csc x – 2 = 0 a. b. c. d. {0} { 0, } ____ 33. Given: , angle A is in Quadrant I and angle B is in Quadrant II. Find the values of the following: tan (A + B) a. b. c. d. ____ 34. Given: tan A = , and cos B = , for A and B in quadrant III. Find the values of the following: tan 2A a. b. c. d. ____ 35. What is the phase shift of y = cos (x + a. to the right b. to the left c. to the left d. to the right )? ____ 36. What is the variation of this function? y = cos Θ; a. b. c. d. to Increases from 0 to 1. Increases through all negative values to 0. Decreases through all positive values to 1. Decreases from 0 to −1. ____ 37. What are the extreme values ofy = cos (x + a. b. 1 and – 1 and – c. d. 4 and −4 )? and – ____ 38. Find the solution set of each equation in the interval: 0 ≤ x < 2 . tan x + 1 = 0 a. b. c. d. ____ 39. Evaluate the expression: a. b. c. d. ____ 40. Find the solution set of 0 ≤ x < 2 a. in the interval cos x + sin x = 1. { ,2 } b. c. d. {0} ____ 41. Find the inverse of y = 5. a. b. c. y=5 x=5 d. x = −5 y= ____ 42. What is one identity you could use to convert the LHS: a. b. c. d. ____ 43. Evaluate 2 sin 67.5° cos 67.5°. What is the second step equal to? a. b. sin 2(67.5°) c. d. cos 2 (67.5°) ? ____ 44. Given , which is in quadrant I, find . a. b. c. d. ____ 45. Reduce the following expression to a single function of one angle: cos(45° + A) + cos(45° − A). a. b. c. d. ____ 46. Evaluate the expression: a. b. c. d. 0 1 −1 ____ 47. What are the extreme values of a. b. c. 3 and −3 2 and −2 d. 1 and −1 ? ____ 48. Reduce each of the following expressions to a single function of one angle: a. b. c. d. tan 20° tan 30° tan 60° tan 40° ____ 49. Evaluate 2 sin 67.5° cos 67.5°. What is the value? a. b. 0.5556 c. d. 0.8315 . ____ 50. Find the solution set of each equation in the interval: 0 ≤ x < 2 . 4 cos2x = 2 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. The University of Nebraska is an equal opportunity educator and employer. ©2019, The Board of Regents of the University of Nebraska. All rights reserved. Precalculus 2: Trigonometry Summary of Formulas Functions of the sum and difference of two angles: cos (A – B) = cos A cos B + sin A sin B cos (A + B) = cos A cos B – sin A sin B sin (A + B) = sin A cos B + cos A sin B sin (A – B) = sin A cos B – cos A sin B tan A + tan B tan (A + B) = 1 – tan A tan B tan A – tan B tan (A – B) = 1 + tan A tan B Functions of twice an angle (double-angle formulas): cos 2A = cos2 A – sin2 A = 1 – 2 sin2 A = 2 cos2 A – 1 sin 2A = 2 sin A cos A tan 2A = 2 tan A 1 – tan2 A Functions of half an angle (half-angle formulas): Tables MTHH 044 Product formulas: 2 sin A cos B = sin (A + B) + sin (A – B) 2 cos A sin B = sin (A + B) – sin (A – B) 2 cos A cos B = cos (A + B) + cos (A – B) 2 sin A sin B = cos (A – B) – cos (A + B) Sum formulas: Tables Included in this section are three sets of tables. The first is the Table of Trigonometric Functions for angles written in degrees. The second is the Table of Trigonometric Functions for angles written in radians. The third table is a table of Logarithmic Functions. Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Table 3 - Logarithms of Numbers Tables MTHH 044 Tables MTHH 044 ...
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