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LHS CAT4e ISM-05-final - Chapter 5 TRIGONOMETRIC FUNCTIONS...

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467 Chapter 5 TRIGONOMETRIC FUNCTIONS Section 5.1: Angles 1. 30° (a) 90 30 60 ° − ° = ° (b) 180 30 150 ° − ° = ° 2. 60° (a) 90 60 30 ° − ° = ° (b) 180 60 120 ° − ° = ° 3. 45° (a) 90 45 45 ° − ° = ° (b) 180 45 135 ° − ° = ° 4. 18° (a) 90 18 72 ° − ° = ° (b) 180 18 162 ° − ° = ° 5. 54° (a) 90 54 36 ° − ° = ° (b) 180 54 126 ° − ° = ° 6. 89° (a) 90 89 1 ° − ° = ° (b) 180 89 91 ° − ° = ° 7. (a) 90 1 89 ° − ° = ° (b) 180 1 179 ° − ° = ° 8. 10° (a) 90 10 80 ° − ° = ° (b) 180 10 170 ° − ° = ° 9. 14 20 ° (a) 90 14 20 89 60 14 20 75 40 ° − ° = ° ° = ° (b) 180 14 20 179 60 14 20 165 40 ° − ° = ° ° = ° 10. 39 50 ° (a) 90 39 50 89 60 39 50 50 10 ° − ° = ° ° = ° (b) 180 39 50 179 60 39 50 140 10 ° − ° = ° ° = ° 11. 20 10 30 ° ′′ (a) 90 20 10 30 89 59 60 20 10 30 69 49 30 ° − ° = ° ° ′′ ′′ ′′ = ° ′′ (b) 180 20 10 30 179 59 60 20 10 30 159 49 30 ° − ° ′′ = ° ° ′′ ′′ = ° ′′ 12. 50 40 50 ° ′′ (a) 90 50 40 50 89 59 60 50 40 50 39 19 10 ° − ° = ° ° ′′ ′′ ′′ = ° ′′ (b) 180 50 40 50 179 59 60 50 40 50 129 19 10 ° − ° ′′ = ° ° ′′ ′′ = ° ′′ 13. The two angles form a straight angle. 7 11 180 18 180 10 x x x x + = = = The measures of the two angles are ( ) ( ) 7 7 10 70 x ° = ° = ° and ( ) ( ) 11 11 10 110 . x ° = ° = ° 14. The two angles form a straight angle. ( ) ( ) 20 10 3 9 180 23 19 180 23 161 7 x x x x x + + + = + = = = The measures of the two angles are ( ) ( ) 20 10 20 7 10 150 x + ° = + ° = ° and ( ) ( ) 3 9 3 7 9 30 . x + ° = + ° = ° 15. The two angles form a right angle. 4 2 90 6 90 15 y y y y + = = = The two angles have measures of ( ) ( ) 4 4 15 60 y ° = ° = ° and ( ) ( ) 2 2 15 30 . y ° = ° = ° 16. The two angles form a right angle. ( ) ( ) 5 5 3 5 90 8 10 90 8 80 10 k k k k k + + + = + = = = The measures of the two angles are ( ) ( ) ( ) 5 5 5 10 5 50 5 55 k + ° = + ° = + ° = ° and ( ) ( ) ( ) 3 5 3 10 5 30 5 35 . k + ° = + ° = + ° = °
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468 Chapter 5: Trigonometric Functions 17. The two angles form a straight angle. ( ) ( ) 4 14 180 18 180 10 x x x x + − = ⇒ − = = − The measures of the two angles are ( ) ( ) 4 4 10 40 x ° = ° = ° and ( ) ( ) 14 14 10 140 . x ° = ° = ° 18. The two angles form a straight angle. 9 9 180 18 180 10 x x x x + = = = The measure of each of the angles is 9 10 90 ° = ° . 19. The sum of the measures of two supplementary angles is 180°. ( ) ( ) 10 7 7 3 180 17 10 180 17 170 10 x x x x x + + + = + = = = The measures of the two angles are ( ) ( ) ( ) 10 7 10 10 7 100 7 107 x + ° = + ° = + ° = ° and ( ) ( ) 7 3 7 10 3 x + ° = + ° ( ) 70 3 73 = + ° = ° . 20. The sum of the measures of two supplementary angles is 180°. ( ) ( ) 6 4 8 12 180 14 16 180 14 196 14 x x x x x + = = = = The measures of the two angles are ( ) ( ) ( ) 6 4 6 14 4 84 4 80 x ° = ° = ° = ° and ( ) ( ) 8 12 8 14 12 x ° = ° ( ) 112 12 100 = ° = ° .
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