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Name _______________________________________ Date __________________ Class __________________ Practice A The Unit Circle Convert each measure from degrees to radians or from radians to degrees. 2. 1. 60 radians 60 _______________ 180 3. 5 6 2 5 2 180 5 radians _______________ 5. 4. 315 ________________________ 6. 105 ________________________ 9. 300 ________________________ ________________________ 7. 4 3 ________________________ 8. ________________________ 10. 10 3 6 6 ________________________ 11. ________________________ 16 9 ________________________ Find the exact value of each trigonometric function. Use the unit circle. 12. sin 60 a. At what point on the unit circle does the angle terminate? ___________________ b. Use sin y. ___________________ 13. cos 5 3 ________________________ 16. sin 330 ________________________ 15. tan 14. tan 225 ________________________ 17. cos 150 ________________________ 18. tan 240 ________________________ ________________________ Solve. 19. John is adding a curved edge to the landscaping in front of the high school. The curve is an arc of a circle with a radius of 1600 feet. The central angle that intercepts the curve measures radians. 8 Find the length of the curve to the nearest foot. ________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ subtracting 360 from the measure of the angle Problem Solving 1. 180 2. 60 330 60 min 360 b. 55 min c. 25 min 3. a. 6. Yes; because by definition, reference angles are the measure of the positive acute angle made by the terminal side of an angle and the x-axis. THE UNIT CIRCLE d. 150 Practice A 4. a. 2 h 20 min radians 3 2. 72 1 b. 2 3 1. c. 60 3. 150 4. 5. 135 6. 7. 240 8. 30 5. a. tan 3 2 b. 2.2 km 6. A 7. J Reading Strategy 1. Possible answer: The angle is positive and measures between 180 and 270. 2. Possible answer: The angle is negative and measures between 270 and 360. 3. a. 9. 5 radians 3 c. 65 4. a. b. 160 c. 20 5. Yes; because you can find coterminal angles by either adding 360 to or 7 radians 12 10. 18 radians 11. 320 1 3 12. a. , 2 2 3 2 b. 1 2 14. 1 15. 0 16. 1 2 18. 3 13. 17. b. 115 7 radians 4 3 2 19. 628 ft Practice B 43 radians 36 1. 75 2. 3. 290 4. radians 5. 300 6. 210 7. 20 radians 9 9. 7 radians 36 11. 1 13. 2 2 8. 54 10. 1 2 12. 3 3 14. 2 2 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry