Calculus Examples

$\arcsin (\sin (\frac{8 π}{3}))$

Step 1

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

$\arcsin (\sin (\frac{2 π}{3}))$

Step 2

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

$\arcsin (\sin (\frac{π}{3}))$

Step 3

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

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

Step 4

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

$\frac{π}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{3}$

Decimal Form:

$1.04719755 \dots$