HLRGAATPreISM_35799X_08_ch8

HLRGAATPreISM_35799X_08_ch8 - Chapter 8: Trigonometric...

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Chapter 8: Trigonometric Functions and Applications 8.1: Angles and Their Measures 1. (a) (b) 2. (a) (b) 3. (a) (b) 4. (a) Since (b) Since 5. (a) Since (b) Since 6. (a) Since (b) Since 7. (a) (b) 8. (a) Since (b) Since 9. Since every 5 minute section is Therefore 5 o’clock equals 10. Since every 1 minute section is Therefore 1:45 equals 20 minutes 11. , therefore the angles are: 12. , therefore the angles are: 13. , therefore the angles are: 14. , therefore the angles are: 15. , therefore the angles are: 6 1 14 2 2 4 5 80° and 8 1 14 2 2 12 5 100°. 1 6 x 2 4 2 1 1 8 x 2 12 2 5 180 1 14 x 2 16 5 180 1 14 x 5 196 1 x 5 14 10 1 10 2 1 7 5 107° and 7 1 10 2 1 3 5 73°. 1 10 m 1 7 2 1 1 7 m 1 3 2 5 180 1 17 m 1 10 5 180 1 17 m 5 170 1 m 5 10 5 1 10 2 1 5 5 55° and 3 1 10 2 1 5 5 35°. 1 5 k 1 5 2 1 1 3 k 1 5 2 5 90 1 8 k 1 10 5 90 1 8 k 5 80 1 k 5 10 2 1 15 2 5 30° and 4 1 15 2 5 60°. 4 y 1 2 y 5 90 1 6 y 5 90 1 y 5 15 7 1 10 2 5 70° and 11 1 10 2 5 110°. 7 x 1 11 x 5 180 1 18 x 5 180 1 x 5 10 23.75 3 5 142.5°. 1 a 3 4 3 5 minutes b or 6°. 360° 4 60 5 6°, 5 3 30° 5 150°. 30°. 360° 4 12 5 30°, 180° 5 π radians, s 1 x 5 π 1 s 5 π 2 x . 90° 5 π 2 radians, c 1 x 5 π 2 1 c 5 π 2 2 x . s 1 x ° 5 180° 1 s 5 1 180 2 x 2 ° c 1 x ° 5 90° 1 c 5 1 90 2 x 2 ° 180° 5 π radians, s 1 π 12 5 π 1 s 5 12 π 12 2 π 12 1 s 5 11 π 12 . 90° 5 π 2 radians, c 1 π 12 5 π 2 1 c 5 6 π 12 2 π 12 1 c 5 5 π 12 . 180° 5 π radians , s 1 π 4 5 π 1 s 5 4 π 4 2 π 4 1 s 5 3 π 4 . 90° 5 π 2 radians, c 1 π 4 5 π 2 1 c 5 2 π 4 2 π 4 1 c 5 π 4 . 180° 5 π radians , s 1 π 3 5 π 1 s 5 3 π 3 2 π 3 1 s 5 2 π 3 . 90° 5 π 2 radians, c 1 π 3 5 π 2 1 c 5 3 π 6 2 2 π 6 1 c 5 π 6 . s 1 45° 5 180° 1 s 5 135° c 1 45° 5 90° 1 c 5 45° s 1 60° 5 180° 1 s 5 120° c 1 60° 5 90° 1 c 5 30° s 1 30° 5 180° 1 s 5 150° c 1 30° 5 90° 1 c 5 60°
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16. , therefore the angles are: 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. See Figure 31. The coterminal angles are: and are in quadrant I. 32. See Figure 32. The coterminal angles are: and are in quadrant I. 33. See Figure 33. The coterminal angles are: and are in quadrant II. Figure 31 Figure 32 Figure 33 34. See Figure 34. The coterminal angles are: and are in quadrant III. 35. See Figure 35. The coterminal angles are: and are in quadrant IV. 36. See Figure 36. The coterminal angles are: and are in quadrant III. ] 159° 1 360° 5 201° and ] 159° 2 360° 5] 519°, ] 61° 1 360° 5 299° and ] 61° 2 360° 421°, 234° 1 360° 5 594° and 234° 2 360° 126°, 0 x y 174 ° 0 x y 89 ° 0 x y 75 ° 174° 1 360° 5 534° and 174° 2 360° 186°, 89° 1 360° 5 449° and 89° 2 360° 271°, 75° 1 360° 5 435° and 75° 2 360° 285°, 102.3771° 5 102° 1 .3771 1 60' 2 5 102° 22.626' 5 102° 22' .626 1 60" 2 5 102° 22' 38" 89.9004° 5 89° 1 .9004 1 60' 2 5 89° 54.024' 5 89° 54' .024 1 60" 2 5 89° 54' 1" 59.0854° 5 59° 1 .0854 1 60' 2 5 59° 5.124' 5 59° 5' .124 1 60" 2 5 59° 5' 7" 31.4296° 5 31° 1 .4296 1 60' 2 5 31° 25.776' 5 31° 25' .776 1 60" 2 5 31° 25' 47" 34° 51' 35" 5 34° 51' 35 60 5 34° 51.583' 5 a 34 51.583 60 b ° 5 34.860° 91° 35' 54" 5 91° 35' 54 60 5 91° 35.9' 5 a 91 35.9 60 b ° 5 91.598° 38° 42' 5 a 38 42 60 b ° 5 38.7° 20° 54' 5 a 20 54 60 b ° 5 20.9° 90° 2 36° 18' 47" 5 89° 59' 60" 2 36° 18' 47" 5 53° 41' 13" 90° 2 72° 58' 11" 5 89° 59' 60" 2 72° 58' 11" 5 17° 1' 49" 47° 23' 2 73° 48' 73° 48' 1 47° 23' 1 73° 48' 2 47° 23' 2 26° 25' 71° 18' 2 47° 29' 5 70° 78' 2 47° 29' 5 23° 49' 75° 15' 1 83° 32' 5 158° 47' 62° 18' 1 21° 41' 5 83° 59' 9 1 7 2 1 6 5 69° and 3 1 7 2 5 21°.
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HLRGAATPreISM_35799X_08_ch8 - Chapter 8: Trigonometric...

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