Question

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

$(6.3,3.8)$

Short answer

The rectangular coordinates is $\left(-4.98,-3.85\right)$.

Step-by-step solution

Step 1. Given Information 

We are given polar coordinates of a point,

$(6.3,3.8)$

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,

$$\begin{gathered} x=r\cos \theta \\ =6.3·\cos (3.8) \\ =6.3(-0.7909) \\ =-4.98 \end{gathered}$$

Similarly,

$$\begin{gathered} y=r\sin \theta \\ =6.3\times \sin (3.8) \\ =6.3\times -0.6118 \\ =-3.85 \end{gathered}$$

So, the rectangular coordinates is $\left(-4.98,-3.85\right)$.