Trigonometry Examples

$y = \arcsin (\sin (\frac{3 π}{4}))$

Step 1

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

$y = \arcsin (\sin (\frac{π}{4}))$

Step 2

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

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

Step 3

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

$y = \frac{π}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{π}{4}$

Decimal Form:

$y = 0.78539816 \dots$