Precalculus Examples

$y = \arcsin (\sin (\frac{4 π}{3}))$

Step 1

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

$y = \arcsin (- \sin (\frac{π}{3}))$

Step 2

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$y = \arcsin (- \frac{\sqrt{3}}{2})$

Step 3

The exact value of $\arcsin (- \frac{\sqrt{3}}{2})$ is $- \frac{π}{3}$ .

$y = - \frac{π}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{π}{3}$

Decimal Form:

$y = - 1.04719755 \dots$