Precalculus Examples

$\sin (- \frac{9}{2} \cdot π)$

Step 1

Combine $π$ and $\frac{9}{2}$ .

$\sin (- \frac{π \cdot 9}{2})$

Step 2

Move $9$ to the left of $π$ .

$\sin (- \frac{9 \cdot π}{2})$

Step 3

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

$\sin (\frac{3 π}{2})$

Step 4

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.

$- \sin (\frac{π}{2})$

Step 5

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

$- 1 \cdot 1$

Step 6

Multiply $- 1$ by $1$ .

$- 1$