Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 29
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43Problems:
In Problems 144-146, evaluate each expression using the negative-angle identities.
π
−
=
144.
tan
6
145. cos (90°) + sin (-180°) =
π
π
4
−
−
=
146.
sin
tan
3
3
In Problems 147-149, evaluate each expression using the cofunction identities.
π
=
147.
cos
3
π
3
=
148.
cot
4
149. tan (90° - 45°) + cos (90° - 180°) =
In Problems 150-154, use the sum and difference identities for the cosine function to evaluate each
expression.
π
π
π
=
−
150.
cos
cos
12
3
4
151. cos 105°
π
π
π
π
7
5
7
5
−
152.
cos
cos
sin
sin
12
12
12
12
(
)
1
2
θ
θ
θ
°
−
=
=
−
153.
cos
30
if
sin
and
cos
5
5
π
2
2
θ
θ
θ
+
=
−
=
154.
cos
if
sin
and
cos
4
2
2
π
θ
θ
By replacing
with
-
in the difference and sum identities for the cosine and then applying the
2
cofunction identities, we obtain the sum and difference identities for the sine function:
θ
φ
θ
φ
θ
φ
sin (
+
) = sin
cos
+ cos
sin
and
θ
φ
θ
φ
θ
φ
sin (
-
) = sin
cos
- cos
sin
.
The sum and difference identities for the tangent function are developed from the sum and difference
identities for the sine and cosine and the quotient identities. These identities state that for any angles
θ
φ
and
θ
φ
+
(
)
tan
tan
θ
φ
+
=
tan
θ
φ
−
1
tan
tan
and
θ
φ
−
(
)
tan
tan
θ
φ
−
=
tan
θ
φ
+
1
tan
tan
- 29 -
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