Question

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

$(7.5,{110}^{\circ })$

Short answer

The rectangular coordinates is $(-2.57,7.05)$.

Step-by-step solution

Step 1. Given Information

We are given polar coordinates of a point,

$(7.5,{110}^{\circ })$

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,

$$\begin{gathered} x=r\cos \theta \\ =7.5·\cos 110° \\ =7.5·(-0.3420) \\ =-2.57 \end{gathered}$$

Similarly,

$$\begin{gathered} y=r\sin \theta \\ =7.5·\sin 110° \\ =7.5(0.939) \\ =7.05 \end{gathered}$$

So, the rectangular coordinates is $(-2.57,7.05)$.