Find the Exact Value arcsin(sin((9pi)/12))

$\arcsin (\sin (\frac{9 π}{12}))$

Cancel the common factor of $9$ and $12$ .

Factor $3$ out of $9 π$ .

$\arcsin (\sin (\frac{3 (3 π)}{12}))$

Cancel the common factors.

Factor $3$ out of $12$ .

$\arcsin (\sin (\frac{3 (3 π)}{3 (4)}))$

Cancel the common factor.

$\arcsin (\sin (\frac{3 (3 π)}{3 \cdot 4}))$

Rewrite the expression.

$\arcsin (\sin (\frac{3 π}{4}))$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\arcsin (\sin (\frac{π}{4}))$

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\arcsin (\frac{\sqrt{2}}{2})$

The exact value of $\arcsin (\frac{\sqrt{2}}{2})$ is $\frac{π}{4}$ .

$\frac{π}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{4}$

Decimal Form:

$0.78539816 \dots$