Question

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(-3,\mathrm{\pi })$

Short answer

The rectangular coordinates corresponding to the polar coordinates $(-3,\mathrm{\pi })$are$(3,0)$

Step-by-step solution

Step 1. Given information

The given poplar coordinates of a point$(-3,\mathrm{\pi })$

Step 2. Finding x values 

For a point P on the terminal side of $\theta$and having polar coordinates $(r,\theta )$, the corresponding rectangular coordinates are given by $x=r\cos \theta$and $y=r\sin \theta$.

Substitute -3 for r and$\pi$ for $\theta$in $x=r\cos \theta$ to get the value of x.

$$\begin{gathered} x=r\cos \theta \\ =-3\cos \left(\pi \right) \\ =3 \end{gathered}$$

Step 3. Finding y value 

Substitute $-3$for $x$and $\mathrm{\pi }$for $\theta$ in to get the value of y.

$$\begin{gathered} y=r\sin \theta \\ =-3\sin \left(\pi \right) \\ =0 \end{gathered}$$

Therefore, the rectangular coordinates corresponding to the polar coordinates$(-3,\pi )$are$(3,0)$