LHS CAT4e ISM-05-final

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 1795960 201030 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 504050 129 19 10 ° 13. The two angles form a straight angle. 7 11 180 18 180 10 xx 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 +++ = += =⇒ = The measures of the two angles are ( ) ( ) 20 10 20 7 10 150 x = and ( ) ( ) 39 3 79 3 0 . x = 15. The two angles form a right angle. 429 069 0 1 5 yy y y = The two angles have measures of ( ) ( ) 44 1 5 6 0 y ° and ( ) ( ) 22 1 5 3 0 . y ° 16. The two angles form a right angle. ( ) ( ) 55359 081 09 0 88 0 1 0 kk k ++ += ⇒ + = ⇒ =⇒= The measures of the two angles are ( ) ( ) ( ) 55 5 1 05 5 0 5 5 5 k = = +° and ( ) ( ) ( ) 35 3 1 3 0 5 3 5 . k =
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468 Chapter 5: Trigonometric Functions 17. The two angles form a straight angle. ( ) ( ) 4 14 180 18 180 10 xx 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. 991 8 0 18 180 10 x x += = = The measure of each of the angles is 910 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 ++ += =⇒ = The measures of the two angles are ( ) ( ) ( ) 10 7 10 10 7 100 7 107 x = = and ( ) ( ) 73 7 1 03 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 −+ − = ⇒ −= ⇒ = The measures of the two angles are ( ) ( ) ( ) 64 6 1 44 8 4 4 8 0 x = = −° and ( ) ( ) 81 2 8 1 41 2 x = ( ) 112 12 100 ° = ° . 21. The sum of the measures of two complementary angles is 90°. ( ) 9639 01 269 0 12 84 7 x ++ = ⇒ += ⇒ =⇒= The measures of the two angles are ( ) ( ) ( ) 96 9 76 6 3 6 6 9 x = = +° and ( ) ( ) 33 7 2 1 . x °= ° 22. The sum of the measures of two complementary angles is 90°. ( ) ( ) 35 64 09 094 59 0 9 135 15 x −+ − = ⇒ − = ⇒ = The measures of the two angles are ( ) ( ) ( ) 35 3 1 55 4 5 5 4 0 x = and ( ) ( ) ( ) 6 40 6 15 40 90 40 50 . x = =−° = ° 23. Let x = the measure of the angle. If the angle is its own complement, then we have 90 2 90 45 x x += ⇒ = ⇒= Thus, a 45° angle is its own complement. 24. Let x = the measure of the angle. If the angle is its own supplement, then we have 180 2 180 90 x x Thus, a 90° angle is its own supplement. 25. () ( ) 25minutes 60minutes 360 25 360 25 6 150 60 x x = ° == = ° 26. Since the minute hand is 3 4 the way around, the hour hand is 3 4 of the way between the 1 and 2. Thus, the hour hand is located 8.75 minutes past 12. The minute hand is 15 minutes before the 12. The smaller angle formed by the hands of the clock can be found by solving the proportion ( ) 15 8.75 minutes .
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This note was uploaded on 11/13/2010 for the course MATH MAT 123 taught by Professor Smith during the Spring '10 term at Thomas Edison State.

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

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