Math Right Triangle Trig Test Review Answers

Right Triangle Trigonometry Review Name:________________________________ Hour:_______ Pre-Calculus Convert from radians to degrees or degrees to radians. 1. 40° 2. 7𝜋 3. 145° 6 5. Find the six trig functions of 𝜃 6. If sin 𝜃 = 4. 5 6 11𝜋 4 , find cos 𝜃 and tan 𝜃. ξ7 𝜃 4 Find the exact value for 𝒙. 7. 8. 9. 10 9 30° 45° 𝒙 60° 14 𝒙 𝒙 Evaluate without using a calculator. 10. (sin 45°)2 + (cos 45°)2 𝜋 11. (tan 60°)2 + (csc 45°)2 𝜋 12. sin 4 + cos 4 Solve the triangle. Find all missing sides and angles, as exact values. 13. 4ξ6 45° 14. 60° 38 1 Find the value of 𝒙 and/or 𝒚. Find an exact answer for 𝒙 in #15 and #17 15. 16. 24 𝑥 32 𝑦 48° 60° 17. 80 60° 𝑥 30° Determine the measurements for angle 𝜽 for each of the following triangles. Round to the nearest tenth of a degree. 18. 19. 𝜃 13 20. 6 𝜃 𝜃 11 8 15 12 Applications: Draw a picture for each! Round all answers to the nearest tenth. 21. An airplane is flying at an elevation of 6500 feet, directly above a straight highway. The pilot spots two cars on the highway in front of him. The angle of depression to one car is 23° and the angle of depression to the other car is 18°. How far apart are the cars? 2 22. Find the angle of depression from the top of a treehouse 20 feet above ground to a park bench 40 feet from the base of the tree. 23. A woman is standing on a hill and sees a flagpole that she knows is 60 feet tall. She views the bottom of the flagpole with an angle of depression of 16° and her angle of elevation to the top of the pole is 20°. Find the woman’s distance from the flagpole. 24. A student looks out of a second-story school window and sees the top of the school flagpole at an angle of elevation of 27°. The student is 21 ft above the ground and 75 ft from the flagpole. Find the height of the flagpole. 25. A skateboard ramp touches the ground at one point, and is 4 ft off the ground at its highest point. The angle of elevation the ramp makes with the ground is 18.4°. What is the length of the ramp? 26. An escalator 152 feet in length rises to a platform and makes 30° angle with the ground. Find the height of the platform above the ground. 27. Points 𝐴 and 𝐵 (on the same side of a tower) are 12 m apart. The angles of elevation of the top of a tower are 35° and 45° respectively. Find the tower’s height. 3 28. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 6.5°. After you drive 16 miles closer to the mountain, the angle of elevation is 14°. Approximate the height of the mountain. Find the sign of the expression if the terminal point determined by 𝜽 is in the given quadrant. 29. 31. cos 𝜃 tan 𝜃; QIII tan 𝜃 sin 𝜃 cot 𝜃 ; QII 30. cos 𝜃 sec 𝜃; Any Quadrant 32. 𝑡𝑎𝑛2 𝜃 sec 𝜃; QII From the information given, find the quadrant in which 𝜽 lies. 33. sec 𝜃 > 0 and cot < 0 34. cot 𝜃 > 0 and cos > 0 35. tan 𝜃 > 0 and csc < 0 36. sin 𝜃 > 0 and cot < 0 Find the values of the other trig functions using the given information. 37. sin 𝜃 = 5 ; 13 in Quadrant II 38. tan 𝜃 = − 8 in Quadrant IV 7 39. cot 𝜃 = 40 9 in Quadrant I 40. csc 𝜃 = − 4 in Quadrant III 4 Find the reference angle. 41. 42. 405° 29𝜋 6 43. 840° 44. 16𝜋 5 Find the exact value of the function WITHOUT a calculator. 45. sin 330° 48. tan 51. tan 5𝜋 6 7𝜋 2 46. cot 𝜋 47. cos 315° 49. sec 300° 50. sin 3𝜋 4 52. csc 53. cos 5𝜋 3 19𝜋 6 Are the following points on the unit circle? Show your work. 54. 21 20 (29 , − 29) 55. (− ξ10 3ξ10 , 10 ) 10 The point P is on the unit circle. Find 𝑷(𝒙, 𝒚) from the given information. 56. The 𝑦-coordinate is 8 9 3 and 𝑃 lies 57. The 𝑥-coordinate is − 4 and 𝑃 is in Q3 to the left of the 𝑦-axis Use the reference angles to find the terminal point determined by angle 𝜽. 58. 𝜃=− 2𝜋 3 59. 𝜃= 3𝜋 4 60. 𝜃 = − 225° 5 Answers to Trig Test Review Pre-Calculus 1. 2𝜋 9 2. 3. 210° 29𝜋 36 4. 3 5. 495° sin 𝜃 = 4 cos 𝜃 = 4 csc 𝜃 = 3 sec 𝜃 = 6. ξ11 6 cos 𝜃 = 10. 1 tan 𝜃 = 5ξ11 11 11. 5 7. 8. 𝑥 = 5ξ3 12. ξ2 𝑥= 9ξ2 2 9. 13. 𝑥 = 4ξ6, 𝑦 = 8ξ3 320ξ3 3 cot 𝜃 = 𝑥= 38ξ3 , 3 3ξ7 7 ξ7 3 28ξ3 3 𝑦= 76ξ3 3 16. x = 49.72, 19. 𝜃 = 56.9° 20. 𝜃 = 61.9° 21. 4691.9 ft. 22. 26.6° 23. 92.2 ft. 24. 59.2 ft. 25. 12.7 ft. 26. 76 ft. 27. 28.03 m 28. 3.4 mi. 29. Negative 30. Positive 31. Positive 32. Negative 33. Q4 35. Q3 38. sin 𝜃 = 36. Q2 40. sin 𝜃 = 5 37. sin 𝜃 = 13 cos 𝜃 = −7ξ113 113 cos 𝜃 = 8ξ113 113 9 40 tan 𝜃 = 40 −ξ15 4 tan 𝜃 = 39. sin 𝜃 = 41 cos 𝜃 = 41 −1 4 cos 𝜃 = 41. 𝜃 = 45° 42. 𝜃 = 60° 49. 2 50. ξ2 2 57. 𝑦 = − ξ7 4 1 5 ξ113 −7 9 csc 𝜃 = 41 9 sec 𝜃 = 40 ξ15 15 csc 𝜃 = −4 𝜋 44. 𝜃 = 5 45. − 2 52. -2 53. 2 59. (− 𝜋 ξ2 ξ2 , 2 2 ) sec 𝜃 = 60. (− 13 5 sec 𝜃 = sec 𝜃 = ξ113 8 cot 𝜃 = −7 41 cot 𝜃 = 40 9 −4ξ15 15 cot 𝜃 = ξ15 1 1 18. 𝜃 = 67.4° tan 𝜃 = −12 csc 𝜃 = csc 𝜃 = 43. 𝜃 = 6 ξ3 ) 2 −12 13 −7 8 tan 𝜃 = 51. Undefined 58. (− 2 , − 17. 𝑥 = 14. 𝑥 = tan 𝜃 = 15. 𝑥 = 16ξ3 34. Q1 y = 36.95 ξ7 4 4ξ7 7 ξ2 ξ2 , 2 2 cot 𝜃 = −12 5 8 46. Undefined 54. Yes −13 12 47. 55. Yes ξ2 2 48. − ξ3 3 56. 𝑥 = − ξ17 9 ) 6