Question

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

$(-3,-90°)$

Short answer

The rectangular coordinates corresponding to the polar coordinates $(-3,-90°)$are $(0,3)$

Step-by-step solution

Step 1.Given information

The given poplar coordinates of a point$(-3,-90°)$

Step 2.Finding the value of x

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 $-90°$for $\theta$in $x=r\cos \theta$ to get the value of x.

$$\begin{gathered} x=r\cos \theta \\ =-3.\cos (-90°) \\ =-3.0 \\ =0 \end{gathered}$$

Step 3.Finding the value y.

Substitute $-3$ for r and $-90°$for $\theta$in $y=r\sin \theta$ to get the value of y.

$$\begin{gathered} y=r\sin \theta \\ =-3.\sin (-90°) \\ =3 \end{gathered}$$

Therefore, the rectangular coordinates corresponding to the polar coordinates$(-3,-90°)$are$(0,3)$.