Trigonometry Examples

$\arcsin (\sin (\frac{7 π}{6}))$

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.

$\arcsin (- \sin (\frac{π}{6}))$

Step 2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\arcsin (- \frac{1}{2})$

Step 3

The exact value of $\arcsin (- \frac{1}{2})$ is $- \frac{π}{6}$ .

$- \frac{π}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{6}$

Decimal Form:

$- 0.52359877 \dots$