Question

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

$\left(8.1,5.2\right)$

Short answer

The rectangular coordinates is $\left(3.807,-7.047\right)$.

Step-by-step solution

Step 1. Given Information 

We are given polar coordinates of a point,

$\left(8.1,5.2\right)$

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,

$$\begin{gathered} x=r\cos \theta \\ =8.1\cos \left(5.2\right) \\ =8.1\times (0.47) \\ =3.807 \end{gathered}$$

Similarly,

$$\begin{gathered} y=r\sin \theta \\ =8.1\sin \left(5.2\right) \\ =8.1\times (-0.87) \\ =-7.047 \end{gathered}$$

So, the rectangular coordinates is $\left(3.807,-7.047\right)$.