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MATH 2412 - Precalculus - Trigonometry Exercises
In Problems 1-4, determine the angle A in [0,2π), rounded to the nearest thousandth.
1. sin A = –0.437, with A in Q III
2. cos A = –0.892, with A in Q II
3. tan A = –4.815, with A in Q II
4. csc A = –6.287, with A in Q IV
In Problems 5 and 6, use a sum or difference formula to write the given expression as a single
trigonometric function of a single angle.
5. sin34°cos49° − sin49°cos34°
6. sin15°sin 7°− cos15°cos7°
7. Given tan A = 34 with A in Q III and sinB = − 12 with B in Q III, determine (a) sin(A + B) ,
(b) cos(A − B) , and (c) tan( A + B) .
8. Given sin A = − 45 with A in Q III, determine (a) sin2A , (b) cos2A , and (c) tan 2A .
In Problems 9 and 10, prove the given identity by transforming one side of the equation into
the other.
9. sin(π − β ) = sin β
10. cos x + π2 = − sin x
(
)
In Problems 11 and 12, use a double-angle or half-angle formula to write the given expression
as a single trigonometric function of a single angle.
2
2
11. sin 48°− cos 48°
12.
1− cos π6
1 + cos π6
A
A
13. Given sin A = − 23 with A in Q IV, determine (a) sin A
2 , (b) cos 2 , and (c) tan 2 .
In Problems 14-20, solve for x in [0,2π).
3
14. sin x + cos x = 0
15. cos x = cos x
17. sin2x = 1
18. sin2x + cos x = 0
2
20. 2cos x + 2cos2x = 1
Answers
1. 3.594
7. (a)
2. 2.673
3 3+ 4
10
, (b)
3. 1.776
4 3+ 3
10
5. sin(−15°) or − sin15°
4. 6.123
, and (c) 3 3+ 4
4 3−3
(
= cos x(0) − sin x(1)
= − sin x
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π
12. tan 12
15. 0, π2 ,π, 32π
16. 0, π3 , 53π
13. (a)
17. π4 , 54π
)
10. cos x + π2 = cosx cos π2 − sin x sin π2
= sin β
11. − cos96°
6. − cos22°
7
24
8. (a) 24
25 , (b) − 25 , (c) − 7
9. sin(π − β ) = sinπ cos β − cosπ sin β
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= (0)cos β − (−1)sin β
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2
16. 2sin x + 3cos x = 3
19. sin x = cos2x
3− 5
6 , (b)
3+ 5
6 , (c) −
3π ,
18. π2 , 76π , 2 , 116π 1 9.
−
3− 5
or −3+2 5 14. 34π , 74π
3+ 5
5π ,
π , 5π , 3π
20. π4 , 34π , 4 , 74π
6 6 2