Find the Exact Value sin(pi/2-(3pi)/2)

$\sin (\frac{π}{2} - \frac{3 π}{2})$

Step 1

Combine the numerators over the common denominator.

$\sin (\frac{π - 3 π}{2})$

Step 2

Subtract $3 π$ from $π$ .

$\sin (\frac{- 2 π}{2})$

Step 3

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 π$ .

$\sin (\frac{2 (- π)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$\sin (\frac{2 (- π)}{2 (1)})$

Cancel the common factor.

$\sin (\frac{2 (- π)}{2 \cdot 1})$

Rewrite the expression.

$\sin (\frac{- π}{1})$

Divide $- π$ by $1$ .

$\sin (- π)$

Step 4

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

$\sin (0)$

Step 5

The exact value of $\sin (0)$ is $0$ .

$0$