Question

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

$(-2,-180°)$

Short answer

The rectangular coordinates corresponding to the polar coordinates$(-2,180°)$are$(2,0)$

Step-by-step solution

Step 1.Given information

The given poplar coordinates of a point$(-2,-180°)$

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 $-2$ for r and $-180°$for $\theta$in $x=r\cos \theta$ to get the value of x.

$$\begin{gathered} x=r\cos \theta \\ =-2.\cos (-180°) \\ =-2.(-1) \\ =2 \end{gathered}$$

Step 3.Finding the value of y.

Substitute $-2$ for r and $-180°$for $\theta$in $y=r\sin \theta$to get the value of y.

$$\begin{gathered} y=r\sin \theta \\ =-2.\sin (-180°) \\ =-2.-\sin 180° \\ =-2.0 \\ =0 \end{gathered}$$

Therefore, the rectangular coordinates corresponding to the polar coordinates$(-2,-180°)$are$(2,0)$.