Precalculus Examples

$\arcsin (\sin (\frac{- 2 π}{3}))$

Step 1

Move the negative in front of the fraction.

$\arcsin (\sin (- \frac{2 π}{3}))$

Step 2

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

$\arcsin (\sin (\frac{4 π}{3}))$

Step 3

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.

$\arcsin (- \sin (\frac{π}{3}))$

Step 4

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

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

Step 5

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

$- \frac{π}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{3}$

Decimal Form:

$- 1.04719755 \dots$