Finding Coterminal Angle of the following angle

Consider the given angle:

\(\theta  =  - \frac{{9\pi }}{4}\)

Now, the positive coterminal will be:

\(\begin{array}{c}\theta  =  - \frac{{9\pi }}{4} + 2\pi \\ = \frac{{ - 9\pi  + 8\pi }}{4}\\ =  - \frac{\pi }{4}\end{array}\)

So, the positive coterminal angle is\({ - \frac{\pi }{4}}\).

So, the positive coterminal angle is

\(\begin{array}{c}\theta  =  - \frac{{9\pi }}{4} - 2\pi \\ = \frac{{ - 9\pi  - 8\pi }}{4}\\ =  - \frac{{17\pi }}{4}\end{array}\)

Now, the negative coterminal will be:

\({ - \frac{{17\pi }}{4}}\)