Question

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

$\left(-3.1,182°\right)$

Short answer

The rectangular coordinates is $(3.098,0.093)$.

Step-by-step solution

Step 1. Given Information 

We are given polar coordinates of a point,

$\left(-3.1,182°\right)$

The rectangular coordinates are given by $x=r\cos \theta$and

$y=r\sin \theta$

Step 2. Finding the rectangular coordinates

The rectangular coordinates is given by,

$$\begin{gathered} x=r\cos \theta \\ =-3.1\cos \left(182°\right) \\ =-3.1\times (-0.9994) \\ =3.098 \end{gathered}$$

Similarly,

$$\begin{gathered} y=r\sin \theta \\ =-3.1\sin \left(182°\right) \\ =-3.1\times (-0.03) \\ =0.093 \end{gathered}$$

So, the rectangular coordinates is $(3.098,0.093)$.