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Mathematics
Nolan Johnson
17 March, 05:08
What is the exact value of cos (67.5°) ?
+4
Answers (
1
)
Jared
17 March, 06:45
0
0.38268343
Step-by-step explanation:
cos (67.5)
Rewrite
67.5
as an angle where the values of the six trigonometric functions are known divided by 2. cos (135 / 2)
Apply the cosine half-angle identity.
±
√
1
+
cos
(
135
)
2
Change the
±
to
+
because cosine is positive in the first quadrant.
√
1
+
cos
(
135
)
2
Simplify
√
1
+
cos
(
135
)
2
√
2
-
√
2
2
The result can be shown in multiple forms.
Exact Form:
√
2
-
√
2
2
Decimal Form:
0.38268343
...
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