Trigonometry Examples

$\arcsin (\cos (\frac{5 π}{4}))$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$\arcsin (- \cos (\frac{π}{4}))$

Step 2

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

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

Step 3

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

$- \frac{π}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{4}$

Decimal Form:

$- 0.78539816 \dots$