How do I simplify a radical within a radical in this half-angle problem?

$\mathrm{sin}(-\frac{3\pi}{8})=\pm \sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}$

Delilah Novak
2022-04-18
Answered

How do I simplify a radical within a radical in this half-angle problem?

$\mathrm{sin}(-\frac{3\pi}{8})=\pm \sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}$

You can still ask an expert for help

Ouhamiptkg

Answered 2022-04-19
Author has **18** answers

First, $-\frac{\pi}{2}<-\frac{3\pi}{8}<0$ , so we're in the fourth quadrant and thus sine is negative here. Second:

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

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

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

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

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