MATH 2412 – Precalculus
Related Angle-Sum-DifferenceDouble Angle-Half Angle Formula 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
3
1
, with A in Q III, and sin B = − , with B in Q III, determine (a) sin(A + B) ,
4
2
(b) cos(A − B) , and (c) tan(A + B) .
5. Given tan A =
4
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€6. Given sin A = − , with A in€Q III, determine (a) sin2A , (b) cos2A , and (c) tan2A .
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In Problems 7 and 8, prove the given identity by transforming one side of the equation into the
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other.
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
π
7. sin(π − β ) = sin β
8. cos x +  = −sin x

2
2
A
A
A
9. Given sin A = − , with A in Q IV, determine (a) sin , (b) cos , and (c) tan .
3
2
2
2
10. Use Half-Angle Formulas and exact trig€functions values for 330° to determine exact values for
each of the following: (a) sin165° , (b) cos165° , and (c) tan165° .
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€Answers
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1. 3.594
5. (a)
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2. 2.673
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7. sin(π − β ) = sin π cos β − cos π sin β
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= (0)cos β €
− (−1)sin β
9. (a)
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10. (a)
6. (a)
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2− 3
2− 3
2+ 3
, (b) −
, (c) −
or −2 + 3
€2 + 3
€2
€2
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4. 6.123
24
7
24
, (b) − , (c) −
25
25
7

π
π
π
8. cos x +  = cos x cos − sin x sin

2€
2
2
€ 
= cos x(0) − sin x(1)
= −sin x
3− 5
3− 5
3+ 5
−3 + 5
, (b) −
, (c) −
or
6
6
2
3+ 5 €
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3. 1.776
3 3+4
3 3+4
4 3+3
, (b)
, (c)
10
10
4 3−3
= sin β
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