Answer on Question #48679 – Math – Trigonometry
Find the exact value by using a half-angle identity.
cosine of five pi divided by twelve.
Solution:
We need to find the exact value of the
5𝜋
cos
12
Using a half-angle identity:
5𝜋
5𝜋
1
5𝜋
cos
= cos 6 = ± √ (1 + cos )
12
2
2
6
We know that cos
5𝜋
12
5𝜋
6
=−
√3
2
cos
5𝜋
1 2 √3
=±√ ( − )
12
2 2
2
cos
5𝜋
1 2 − √3
=±√ (
)
12
2
2
cos
5𝜋
2 − √3
=±√
12
4
cos
√2 − √3
5𝜋
=±
12
2
is in quadrant 1 so we choose the «+» sign because cosine is positive there
cos
5𝜋
Answer: cos 12 =
5𝜋 √2 − √3
=
12
2
√2−√3
2
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