Evaluate arcsin(sin((3pi)/2))

$\arcsin (\sin (\frac{3 π}{2}))$

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 fourth quadrant.

$\arcsin (- \sin (\frac{π}{2}))$

Step 2

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

$\arcsin (- 1 \cdot 1)$

Step 3

Multiply $- 1$ by $1$ .

$\arcsin (- 1)$

Step 4

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

$- \frac{π}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{2}$

Decimal Form:

$- 1.57079632 \dots$

Evaluate arcsin(sin((3pi)/2))

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