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 28
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43trigonometric functions of an angle in terms of a point on the terminal side of the angle, it follows that
θ
for any angle
π
π
θ
θ
θ
θ
−
=
−
=
sin
cos
cos
sin
2
2
π
π
θ
θ
θ
θ
−
=
−
=
tan
cot
cot
tan
2
2
These relationships, called the cofunction identities, are also useful in degree form.
θ
θ
θ
θ
sin(90° -
) = cos
cos(90° -
) = sin
θ
θ
θ
θ
tan(90° -
) = cot
cot(90° -
) = tan
Problems:
Memorize the negative-angle identities, the difference and sum identities for the cosine function, and
the cofunction identities. Then, without referring to the statements of these identities, fill in the
missing members of the following identities.
θ
φ
θ
131. cos(
+
) = ______________________
132. ____________________________ = -tan
θ
θ
133. sin (90° -
) = _____________________
134. cos (-
) = _________________________
π
θ
θ
φ
θ
φ
−
=
136.
cot
_______________________
135. ______________ = cos
cos
+ sin
sin
2
θ
θ
φ
θ
φ
137. sin (-
) = _________________________
138. cos
cos
- sin
sin
= _______________
π
θ
θ
−
=
140.
cos
_______________________
139. ___________________________ = -sin
2
θ
θ
φ
141. tan (90° -
) = ____________________
142. cos (
-
) = _______________________
θ
143. tan (-
) = ________________________
We can also use these identities to find values of the trigonometric functions for certain special angles.
Example: Find cos (150°).
(
)
(
)
(
)
3
°
=
°
−
°
=
−
°
=
−
°
=
−
Solution:
cos
150
sin
90
150
sin
60
sin
60
2
π
3
1
θ
θ
θ
+
=
=
Example: Find
cos
,
if
sin
and
cos
.
3
10
10
π
π
π
θ
θ
θ
+
=
−
Solution:
cos
cos
cos
sin
sin
3
3
3
1
1
3
3
=
⋅
−
⋅
2
2
10
10
−
10
3
30
=
20
- 28 -
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