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A2T Review 10.3 Name_____________________________ Convert each measure from degrees to radians or from radians to degrees. 1. 5 12 3. 2. 215 ________________________ 4. 180 ________________________ 5. ________________________ 7. 400 ________________________ ________________________ 5 3 6. ________________________ 8. 29 18 7 6 ________________________ 3 10 9. 35 ________________________ ________________________ Use the unit circle to find the exact value of each trigonometric function. 10. cos 2 3 ________________________ 13. sin 315 ________________________ 11. tan 5 4 12. tan ________________________ 14. cos 225 5 6 ________________________ 15. tan 60 ________________________ ________________________ Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle. 16. 150 ________________________ 19. 11 6 ________________________ 17. 225 18. 300 ________________________ 20. 2 3 ________________________ 21. ________________________ 5 4 ________________________ Solve. 22. San Antonio, Texas, is located about 30 north of the equator. If Earth’s radius is about 3959 miles, approximately how many miles is San Antonio from the equator? ___________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry A2T Review 10.3 Name_____________________________ Problem Solving 1. 180 2. 60 330 60 min 360 b. 55 min c. 25 min 3. a. THE UNIT CIRCLE Practice A d. 150 4. a. 2 h 20 min b. 2 1. 1 3 c. 60 3 5. a. tan 2 b. 2.2 km 6. 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. 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. radians 3 2. 72 7 radians 4 3. 150 4. 5. 135 6. 7. 240 8. 30 9. 5 radians 3 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. 3. a. 17. 3 2 19. 628 ft Practice B b. 115 c. 65 4. a. b. 160 c. 20 5. Yes; because you can find coterminal angles by either adding 360 to or subtracting 360 from the measure of the angle 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 A2T Review 10.3 Name_____________________________ 15. 3 16. 17. 2 2 ; ; 1 2 2 18. 1 3 3 ; 19. ; 2 2 3 21. 2 2 ; ;1 2 2 1 3 3 ; ; 2 2 3 3 1 ; ; 3 2 2 20. 7. 30 8. 300 9. 45 2 2 2 cos 45 2 10. sin 45 3 1 ; ; 3 2 2 tan 45 1 22. 2073 mi 2 2 2 cos 315 2 tan 315 1 11. sin 315 Practice C 5 radians 2 1. 270 2. 3. 50 4. 5. 315 6. 330 1. 6080 ft 2. 1,600,921 mi; 66,705 mi/h 8. 63 3. Area of circle r 2; A sector whose central angle has a measure of radians 7. 35 radians 18 radians 15 37 11. radians 30 9. 1 3 3 ; 13. ; 2 2 3 15. 3 1 ; ; 3 2 2 2 2 ; ;1 17. 2 2 19. 2 2 ; ;1 2 2 1 3 3 ; 21. ; 2 2 3 23. 3 1 ; ; 3 2 2 10 radians 9 Challenge 10. 234 has an area of 7 12. radians 12 circle. So 14. 2 2 ; ; 1 2 2 16. 1 3 3 ; ; 2 2 3 18. 3 1 ; ; 3 2 2 Area of sector 4. 24. b. 3. 4 radians 7 radians 6 5. 240 2. 4. 2 radians 3 6. 270 2 2 or 6 3 2 3 2 6 d. 1.64 in. 2 2 ; ; 1 2 2 5 radians 6 c. S r e. Yes; possible answer: because the arc length of the fragment is very close to the arc length that would be expected for a plate of diameter 25. 138 ft 1. 4 1. a. r 2 2 ; ; 1 2 2 Reteach 1 r 2 r 2 . 2 2 Problem Solving 20. 0; 1; 0 22. times the area of the 2 1 4 3. C 5. B 2. 4. H 6. F Reading Strategy 1. 2 2. 0 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry