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5-1 Trigonometric Identities
Find the value of each expression using the
given information.
1. If cot
= , find tan
.
7. If csc
= and cot = , find sec
.
SOLUTION: SOLUTION: Use the reciprocal identity
to find sin α.
3. If tan
= , find cot
.
Use the quotient identity
to find cos α.
SOLUTION: 5. If cos x =
and sin x =
, find cot x.
SOLUTION: Use the reciprocal identity
to find sec .
7. If csc
= and cot = , find sec
.
SOLUTION: eSolutions Manual - Powered by Cognero
Use the reciprocal identity
α.
to find sin Find the value of each expression using the
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given information.
9. sec and cos ; tan θ = –5, cos > 0
5-1 Trigonometric Identities
Find the value of each expression using the
given information.
9. sec and cos ; tan θ = –5, cos > 0
11. tan
and sin ; sec
= 4, sin > 0
SOLUTION: Use the reciprocal identity
SOLUTION: Use the Pythagorean Identity that involves tan θ to
find sec θ.
to find cos
.
Use the Pythagorean Identity that involves sec
find tan .
Since we are given that cos θ is positive, the
reciprocal function sec θ must be positive, so
.
Use the reciprocal identity
cos θ.
to to find
Since sin θ is positive, and
is positive, tan θ must be positive. Therefore,
to find sin .
Use the quotient identity
11. tan
and sin ; sec
= 4, sin > 0
SOLUTION: Use the reciprocal identity
to find cos
.
13. cos
and tan
; csc = , tan
> 0
SOLUTION: Use the Pythagorean Identity that involves sec
find tan .
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to Use the Pythagorean Identity that involves csc
find cot .
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13. cos
and tan
; csc = , tan
> 0
SOLUTION: 5-1 Use
Trigonometric
Identities
the Pythagorean Identity that involves csc
find cot
to .
15. cot
Since we are given that tan θ is positive, cot θ must
also be positive. Therefore,
Use the reciprocal identity
Use the quotient identity
and sin ; sec
= to find cos
, sin
.
> 0
.
SOLUTION: to find tan Use the Pythagorean Identity that involves sec θ to
find tan .
to find sin Since we are given that sec is negative, we know that cos is negative. We are also given that sin θ
is positive. Since cos is negative and sin is positive, tan is negative. Therefore, .
.
Use the reciprocal identity
.
.
Use the reciprocal identity
to find cot .
Use the quotient identity
to find cos
.
.
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Page 3
.
the reciprocal identity
5-1 Use
Trigonometric
Identities
to find cot .
.
Use the reciprocal identity
to find cos .
Then use the Pythagorean Identity that involves cos
θ to find sin θ. Since we are given that sin θ is positive, sin θ =
.
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