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:
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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
.
to
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 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 .
to
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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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.
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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