Precalculus Examples

$\arcsin (\frac{7 π}{8})$

Since $\frac{7 π}{8}$ is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

$\frac{7 π}{8}$ is not an exact angle

First, rewrite the angle as the product of $\frac{1}{2}$ and an angle where the values of the six trigonometric functions are known. In this case, $\frac{7 π}{8}$ can be rewritten as $(\frac{1}{2}) \cdot \frac{7 π}{4}$ .

$\arcsin ((\frac{1}{2}) \cdot \frac{7 π}{4})$

Multiply $(\frac{1}{2}) \frac{7 π}{4}$ .

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Multiply $\frac{1}{2}$ by $\frac{7 π}{4}$ .

$\arcsin (\frac{7 π}{2 \cdot 4})$

Multiply $2$ by $4$ .

$\arcsin (\frac{7 π}{8})$