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Algebra 2 Honors Name________________ Date_________________ Trig Quiz 1 Review The following problems should be done quickly and without a scientific calculator only. 1. Find the degree measure of an angle 2 Find the degree measure of an angle in standard position determined by the in standard position determined by the rotation of the initial ray through one and rotation of the initial ray through four-fifths two-thirds of a clockwise revolution. of a counter-clockwise revolution. Write a formula for the measures of all angles coterminal with the given angle. Then use the formula to find two angles, one positive and one negative, that are coterminal with the given angle. 3. π = 370° 4. 5π 7 Express in either βDecimal Degreesβ or in βDegrees Minutes Secondsβ to the nearest second. 5. 73° 2β² 6. 119.35° 7. 16° 14β² 39β²β² 8. 74.89° Find a first-quadrant angle π½, for which an angle four times as large as π½ will be in the given quadrant. 9. Quadrant 1 10. Quadrant 2 11. Quadrant 3 12. Quadrant 4 13. Consider an angle π whose terminal sides passes through (β12, β13). Find the value of all six trigonometric functions. 14. Find the six trig functions of π β7 4 5 15. If sin π = 6 , and cos π < 0 find the other five trig functions. Find the exact value for π πππ π. 16. 17. 18. 60° 9 10 π 45° 14 π 30° π 19. 20. 32 24 π¦ 45° 21. 80 Determine the measurements for angle π½ for each of the following triangles. Round to the nearest hundredth of a degree. 22. 23. 24. 6 π 13 π π 11 15 12 Draw a picture for each! Round all answers to the nearest thousandth. 25. An airplane is at an elevation of 35,000 ft when it begins its approach to an airport. Its angle of descent is 6°. What is the approximate air distance between the plane and the airport? 8 26. Find the measures of the acute angles of a right triangle whose legs are 9 cm and 16 cm long. 27. Find the measures of the angles of an isosceles triangle whose sides are 5, 10, and 10. 28. An engineer builds a 75-foot vertical cellular phone tower. Find the angle of elevation to the top of the tower from a point on level ground 95 feet from its base. 29. Points π΄ and π΅ (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 towerβs height. 30. 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. 31. 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. Convert from Radians to Degrees, or Degrees to Radians 32. 40° 33. 7π 34. 145° 6 35. 11π 4 Find the sign of the expression if the terminal point determined by π½ is in the given quadrant. 36. cos π tan π; QIII 38. tan π sin π cot π 37. cos π sec π; Any Quadrant 39. π‘ππ2 π sec π; QII ; QII From the information given, find the quadrant in which π½ lies. 40. sec π > 0 and cot < 0 41. cot π > 0 and cos > 0 42. tan π > 0 and csc < 0 43. sin π > 0 and cot < 0 Find the reference angle. 44. 405° 45. 840° 46. 29π 6 47. Find the exact value of the function without a calculator. 48. sin 330° 49. cot π 51. tan 5π 6 52. sec 300° 54. tan 7π 2 55. csc 50. cos 315° 19π 6 Are the following points on the unit circle? Show your work. 21 57. ( 29 20 , β 29) 16π 5 58. (β β10 3β10 , 10 ) 10 53. sin 3π 4 56. cos 5π 3 Answers 1. β600° 4. 5π 7 7. 16.24° 288° 2. + 2ππ π€βπππ π ππ ππ πππ‘ππππ; 11. 45° < π < 67.5° 13. sin π = β 13β313 , 313 3 4 cos π = β β7 , 4 15. sin π = 6 , cos π = β 17. π₯ = 9β2 2 22. π = 67.38° πππ β 9π 7 73.03° 5. 6. 0° < π < 22.5° 9. 10° πππ β350° 119° 21β² 0β²β² 10. 22.5° < π < 45° 12. 67.5° < π < 90° 14. sin π = , cos π = 5 19π 7 74° 53β² 24β²β² 8. 370 + 360π π€βπππ π ππ ππ πππ‘ππππ; 3. 12β313 , 313 tan π = β11 , 6 3β7 , 7 tan π = β 18. π₯ = 28β3 3 23. π = 56.94° 13 tan π = 12 , csc π = β 4 3 csc π = , sec π = 5β11 , 11 β313 , 13 sec π = β 4 β7 , cot π 7 6 csc π = 5 , sec π = β = β313 , cot π 12 12 = 13 β7 3 6β11 , cot π 11 =β β11 5 64β6 3 19. π₯ = 16β3 20. π₯ = 24. π = 61.93° 25. 334,837.028 ππππ‘ 16. π₯ = 5β3 21. π₯ = 320β3 3 26. π = 29.36° πππ π = 60.64° 27. 75.52° , 75.52° , 28.96° 29. 28.0276 π 30. 59.21 ππππ‘ 31. 3.357 πππππ 32. 35. 495° 36. πππππ‘ππ£π 37. πππ ππ‘ππ£π 38. πππ ππ‘ππ£π 39. πππππ‘ππ£π 40. ππ’ππππππ‘ 4 41. ππ’ππππππ‘ 1 42. ππ’ππππππ‘ 3 43. ππ’ππππππ‘ 2 44. 45° 45. 60° 46. 49. πππππππππ 50. 54. πππππππππ 55. β2 34. 29π 36 β2 2 π 6 51. β 56. 1 2 47. β3 3 28. 38.29° 2π 9 π 5 52. 2 33. 210° 1 48. β 2 53. 57-58. πππ , (π ππ π€πππ) β2 2