Question

Find the exact value by using a half-angle identity. sine of seven pi divided by eight.

Answer 1

− √ 2 − √ 2

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2

Explanation:

Answer 2

`\sin^2\frac{7\pi}8=\frac{1-\cos\frac{7\pi}4}2=\frac{1-\frac1{\sqrt2}}2=(\sqrt2-1)/(2\sqrt2)`

Since
`\frac{7\pi}8` lies in the interval
`0<x<\pi`, and
`\sin x>0` in this interval, you know that when you take the square root, you should consider the positive root only.

So,


`\sin\frac{7\pi}8=\sqrt{(\sqrt2-1)/(2\sqrt2)}`