Precalculus (6th Edition) Blitzer

Step I: Add $2\pi$ to the angle and keep r unchanged. Step II: Add $\pi$ to the angle and replace r with $-r$.
Consider a point $\left( r,\theta \right)$. To find two additional sets of polar coordinates for the point $\left( r,\theta \right)$ we need to follow the steps given below: Step I: Add $2\pi$ to the angle and keep r unchanged. Step II: Add $\pi$ to the angle and replace r with $-r$. For example, consider a point $\left( 2,\frac{\pi }{3} \right)$. Its two additional sets obtained by the steps given above are, $\left( 2,\frac{7\pi }{3} \right)$ from Step I and $\left( -2,\frac{4\pi }{3} \right)$ from Step II.