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Trigonometric Sum Identities Answers

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Which set of steps can be used to prove the sine sum identity, sin(x + y) = sin(x)cos(y) + cos(x)sin(y)?

A
Use the complementary relationship between sine and cosine to rewrite sin(x + y) as . Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
Option A
B
Use the complementary relationship between sine and cosine to rewrite sin(x + y) as . Apply the cosine sum identity. Then simplify using sin(–y) = sin(y) and cos(–y) = –cos(y).
Option B
C
Use the supplementary relationship between sine and cosine to rewrite sin(x + y) as . Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
Option C
D
Use the supplementary relationship between sine and cosine to rewrite sin(x + y) as . Apply the cosine sum identity. Then simplify using sin(–y) = sin(y) and cos(–y) = –cos(y).
Option D
2
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What is the exact value of cos(195°)?

A
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot
Option A
B
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
Option B
C
StartFraction negative StartRoot 6 EndRoot minus StartRoot 2 EndRoot
Option C
D
StartFraction negative StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
Option D
3

Which expression is equivalent to sin(84°)cos(43°) + cos(84°)sin(43°)?

A
sin(41°)
B
cos(41°)
C
sin(127°)
D
cos(127°)
4

Which steps can be used to verify that tan(w + ) = tan(w)?

Question illustration
A
Rewrite tan(w + ) as tan(w) + tan(). Then simplify the expression using tan() = 1.
Option A
B
Rewrite tan(w + ) as tan(w) + tan(). Then simplify the expression using tan() = 0.
Option B
C
Rewrite tan(w + ) using the tangent sum identity. Then simplify the resulting expression using tan() = 1.
Option C
D
Rewrite tan(w + ) using the tangent sum identity. Then simplify the resulting expression using tan() = 0.
Option D
5

Oliver incorrectly states that the expression can be simplified as –1. Review Oliver’s work. = –1

Question illustration
A
The expression does not simplify to –1.
Option A
B
The expression does not have a value of –1.
Option B
C
The expression simplifies to , not .
Option C
D
The expression is equivalent to , not .
Option D
6

What is the exact value of sin(345°)?

A
StartFraction StartRoot 3 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction
Option A
B
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
Option B
C
StartFraction negative StartRoot 3 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction
Option C
D
StartFraction negative StartRoot negative 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
Option D
7

Which expression is equivalent to for all values of r?

Question illustration
A
sin(r)
B
cos(r)
C
–sin(r)
D
–cos(r)
8

Solve the equation over the interval [0, 2].

Question illustration
A
only
Option A
B
only
Option B
C
StartFraction pi over 6 EndFraction and StartFraction 7 pi Over 6 EndFraction
Option C
D
StartFraction 5 pi Over 6 EndFraction and StartFraction 11 pi over 6 EndFraction
Option D
9

What is the exact value of sin(v + w), given , , v is an angle in Quadrant III, and w is an angle is Quadrant IV?

Question illustration
A
StartFraction negative 30 + 4 StartRoot 21 EndRoot Over 55 EndFraction
Option A
B
StartFraction negative 30 minus 4 StartRoot 21 EndRoot Over 55 EndFraction
Option B
C
StartFraction negative 33 + 5 StartRoot 21 EndRoot Over 55 EndFraction
Option C
D
StartFraction negative 33 minus 5 StartRoot 21 EndRoot Over 55 EndFraction
Option D
10

Which numbers complete the blanks when solving the equation over the interval [0, 2]?

Question illustration
A
1; 0
B
0; 1
C
–1; 0
D
0; –1

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