Simplify arcsin(cos(-pi/4))

$\arcsin (\cos (- \frac{π}{4}))$

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\arcsin (\cos (\frac{7 π}{4}))$

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

$\arcsin (\cos (\frac{π}{4}))$

The exact value of $\cos (\frac{π}{4})$ 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:

$0.78539816 \dots$