Find the Reference Angle -(15pi)/2

$- \frac{15 π}{2}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{15 π}{2}$ .

Add $2 π$ to $- \frac{15 π}{2}$ .

$- \frac{15 π}{2} + 2 π$

The resulting angle of $- \frac{11 π}{2}$ is coterminal with $- \frac{15 π}{2}$ but isn\'t positive. Repeat the step.

$- \frac{11 π}{2}$

Add $2 π$ to $- \frac{11 π}{2}$ .

$- \frac{11 π}{2} + 2 π$

The resulting angle of $- \frac{7 π}{2}$ is coterminal with $- \frac{15 π}{2}$ but isn\'t positive. Repeat the step.

$- \frac{7 π}{2}$

Add $2 π$ to $- \frac{7 π}{2}$ .

$- \frac{7 π}{2} + 2 π$

The resulting angle of $- \frac{3 π}{2}$ is coterminal with $- \frac{15 π}{2}$ but isn\'t positive. Repeat the step.

$- \frac{3 π}{2}$

Add $2 π$ to $- \frac{3 π}{2}$ .

$- \frac{3 π}{2} + 2 π$

The resulting angle of $\frac{π}{2}$ is positive and coterminal with $- \frac{15 π}{2}$ .

$\frac{π}{2}$

Step 2

Since $\frac{π}{2}$ is in the first quadrant, the reference angle is $\frac{π}{2}$ .

$\frac{π}{2}$