Question

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

$(6,150°)$

Short answer

The rectangular coordinates corresponding to the polar coordinates$(6,150°)$are$(-3\sqrt{3},3)$

Step-by-step solution

Step 1. Given information

The given poplar coordinates of a point$(6,150°)$

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 $6$for $r$and $150°$ for $\theta$ in to get the value of x .

$$\begin{gathered} x=r\cos \theta \\ =6.\cos (150°) \\ =6.\left(-\frac{\sqrt{3}}{2}\right) \\ =-3\sqrt{3} \end{gathered}$$

Step 3. Find the value of y.

$$\begin{gathered} y=r\sin \theta \\ =6.\sin \left(150°\right) \\ =6.\frac{1}{2} \\ =3 \end{gathered}$$

Therefore, the rectangular coordinates corresponding to the polar coordinates$(6,150°)$are$(-3\sqrt{3},3)$