Question

What is the exact value of cos(7pi/8)

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Answer:

cos ($\frac{7\pi}{8}$) = $-\frac{\sqrt{2+\sqrt{2}}}{2}$

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos $\frac{7\pi}{8}$ = cos $(\pi-\frac{\pi}{8})$ = −cos $\frac{\pi }{8}$

Now using half angle formula, cos(x) = 2 cos²($\frac{\pi }{2}$) − 1, we can write cos $\frac{\pi }{4}$ = 2

cos²($\frac{\pi }{8}$) − 1

This means $\frac{1}{\sqrt{2}}$ + 1 = 2 cos²($\frac{\pi }{8}$)

2 cos²($\frac{\pi }{8}$) = $\frac{\sqrt{2}+1}{\sqrt{2}}$

cos²($\frac{\pi }{8}$) = $\frac{\sqrt{2}+1}{2\sqrt{2}}$

cos($\frac{\pi }{8}$) = $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$

Simplify,

$\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ = $\sqrt{\frac{2+\sqrt{2}}{4}$ = $\frac{\sqrt{2+\sqrt{2}}}{2}$

Hence,

cos ($\frac{7\pi}{8}$) = −cos ($\frac{\pi }{8}$) = $-\frac{\sqrt{2+\sqrt{2}}}{2}$