Question

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

Answer 1

$\sin^2\dfrac{7\pi}8=\dfrac{1-\cos\dfrac{7\pi}4}2=\dfrac{1-\dfrac1{\sqrt2}}2=\dfrac{\sqrt2-1}{2\sqrt2}$

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

So,

$\sin\dfrac{7\pi}8=\sqrt{\dfrac{\sqrt2-1}{2\sqrt2}}$

Answer 2

Answer:

− √ 2 − √ 2

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Step-by-step explanation: