MATH 1112 Trigonometry Final Exam Review 1. Convert 105 to exact radian measure. 2. Convert 2 to radian measure to the nearest hundredth of a radian. 3. Find the length of the arc that subtends an central angle of 150 on a circle if radius 5cm. 4. Find the equivalent number of radians in revolution. 5. A wheel is rotating at 100 revolutions per second. Find the angular velocity in radians per second. 6. Find the area of a sector of a circle with a radius of 10 centimeters and a central angle of 120. Round to the nearest hundredth of a square centimeter, and use the 7. Find the area of the shaded region to the right. Round to the nearest hundredth. 8. If is an acute angle in standard position and, find. 9. Find the exact value of. 10. Find the value of the six trigonometric functions of the angle in standard position with the terminal side passing through the point ( ). 11. Given that key. for an angle in quadrant IV, find the exact value of. 12. Use a calculator to evaluate ( 0 ). Round to four decimal places. 13. Evaluate. 14. State the amplitude and period of the graph of ( ). 15. State the period of the function ( ) 2. 16. Sketch the graph of ( ) 2 ( ). 17. Sketch the graph of ( ) 2. 18. List the minimum point(s) for the graph of ( ) with 0 2. 19. Find the phase shift and period for the function ( ) ( ). 20. Sketch the graph of ( ) 2. 21. Write 2 2 in terms of a single trigonometric function. 12 50 22. Given with in quadrant II and with in quadrant IV, find ( ). 23. Write in terms of a single trigonometric function. 24. Use a half-angle identity to evaluate 22 5. 25. Find the exact value of 2 given and is in quadrant I. 26. Sketch the graph of ( ). 27. Write 2 in terms of a single trigonometric function. 28. Find the exact value of.
29. Find the approximate radian value for ( 0 2 15). 30. Find the approximate degree value for 0 25. 31. Evaluate ( ). 32. Solve for : ( ). 33. Solve the equation 2 1 0 0 0. Round to the nearest tenth. 34. Solve the equation 5 0, 0 0. Round to the nearest tenth. 35. Find the measure of angle of a right triangle if 25cm and 1 cm. 36. Solve triangle if,, and 52in. 37. Find in triangle if 2 m, m, and. 38. In triangle, 110, 10km, and 20km. Find side. 39. In triangle, 21ft, 1 ft, and 25ft. Find angle. 40. Given angle measures 1, side measures 10 yards, and side measures 6 yards, find the area o triangle. Round to the nearest square yard. 41. Given 2 m, 2 m, and 0m, find the area of triangle. Round to the nearest square meter. 42. Find if 5. 43. Write 1 in polar form. 44. Write ( 0 0 ) in standard form. 45. A vector has a magnitude of 12 and a direction of 0. Write its horizontal and vertical components. Round to the nearest tenth. 46. Find the product of 2( 55 55 ) and ( 1 5 1 5 ). 47. Complete the identity. 48. Find the position vector of a vector with initial point ( 2 ) and terminal point (5 ). 49. From the top of a cliff 1,300 feet above sea level, the angle of depression to a ship is 15. What is the distance from the top of the cliff to the ship? Round to the nearest foot. 50. The measure of the angle of elevation from a position 65 feet from the base to the top of a flagpole is 2. Find the height of the flagpole to the nearest tenth of a foot. 51. A boat travels at 55 miles per hours for 1 hour at a bearing of 15. The boat then travels at 50 miles per hour for 2 hours at a bearing of 225. At the end of these 3 hours, how far is the boat from the starting point? Round to the nearest mile. 52. To find the distance across a canyon, a surveying team locates points and on one side of the canyon and point on the other side of the canyon. The distance between and is found to be 92 yards. The angle is 67 and angle is 89. Find the distance across the canyon. Round to the nearest yard. 53. From a certain port, a ship travels 80 miles east and then turns 90 and travels 65 miles to the south. Find the bearing and distance of the ship from port. Round to the nearest tenth. 54. A belt traveling at a rate of 25 feet per second drives a pulley at a speed of 800 revolutions per minute. Find the radius of the pulley to the nearest hundredth of an inch. 55. A car is traveling 55 miles per hour. If the radius of the wheel is 11 inches, find the angular velocity in revolutions per minute.
56. Solve for over the interval 0 2 :. 57. Solve for over the interval 0 2 : ( 2)( 1) 0. 58. Convert ( ), given in polar coordinates, to rectangular coordinates. 59. Convert (2 2), given in rectangular coordinates, to polar coordinates. 60. Find the measure of the angle between vectors and 2 5.
Answers 1. 2. 0.73 3. cm 17. -axis is scaled by, 4. 5. 200 6. 104.72 7. 62.83 8. 9. 10.,, 11. 12. 1 2116 13.,, 14. Amplitude = 3, Period = 4 15. 16. -axis is scaled by,, 18. ( 1) 19. Phase shift = 2, Period = 20. -axis is scaled by, 21. 22. 23. 2 24. 2 1 25.
26. -axis is scaled by, 54. 5 55. 840rpm 56. 0 57. 58. ( ) 59. (2 2 ) 60. 105 27. 28. 29. 1.8666 30. 31. 32. 33. 12, 11 2, 1 2, 2 2 34., 1 1 35. 5 36., 52, 1 37. No solution 38. 25.2km 39. 40. 26 41. 316 42. 43. 2 ( ) 44. 45. 2 1 11 46. 12( 2 0 2 0 ) 47. 48. 10 49. 5,023ft 50. 40.6ft 51. 114mi 52. 208yds 53. 12 1 ( 50 ), 103.1mi