Precalculus (6th Edition) Blitzer

To convert a point from polar to rectangular coordinates or from $\left( r,\theta \right)$ to $\left( x,y \right)$, use one or more of the following identities: $x=r\cos \theta$ $y=r\sin \theta$
To convert a point from polar coordinates to rectangular coordinates or from $\left( r,\theta \right)$ to $\left( x,y \right)$, we will use one or more of the following identities: $x=r\cos \theta$ $y=r\sin \theta$ For example, consider a point $\left( 2,\frac{\pi }{3} \right)$. It can be converted into rectangular coordinates as below: \begin{align} & x=2\cos \frac{\pi }{3} \\ & =2\cdot \frac{1}{2} \\ & =1 \end{align} \begin{align} & y=2\sin \frac{\pi }{3} \\ & =2\cdot \frac{\sqrt{3}}{2} \\ & =\sqrt{3} \end{align} Hence, the polar point $\left( 2,\frac{\pi }{3} \right)$ becomes $\left( 1,\sqrt{3} \right)$ in rectangular coordinates.