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Trigonometric Sum Identities Answers

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If tan m = and tan n = –6, what is the exact value of tan(m + n)?

Question illustration
A
Negative StartFraction 11 Over 2 EndFraction
Option A
B
Negative StartFraction 11 Over 8 EndFraction
Option B
C
StartFraction 11 Over 8 EndFraction
Option C
D
StartFraction 11 Over 4 EndFraction
Option D
2
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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
3

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
4

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
5

Which expression is equivalent to for all values of r?

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

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