Question

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

$(5,300°)$

Short answer

The rectangular coordinates corresponding to the polar coordinates $(5,300°)$are$\left(\frac{5}{2},-\frac{5\sqrt{3}}{2}\right)$

Step-by-step solution

Step 1. Given information

The given poplar coordinates of a point$(5,300°)$

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 5 for r and $300°$for $\theta$ in to get the value of x.

$$\begin{gathered} x=r\cos \theta \\ =5\cos \left(300\right) \\ =\frac{5}{2} \end{gathered}$$

Step 3. Finding the value of y.

Substitute $300°$for $\theta$and 5 for $r$in$y=r\sin \theta$ to get the value of y.

$$\begin{gathered} y=r\sin \theta \\ =5\sin (300°) \\ =-\frac{5\sqrt{3}}{2} \end{gathered}$$

Therefore, the rectangular coordinates corresponding to the polar coordinates $(5,300°)$are$(\frac{5}{2},-\frac{5\sqrt{3}}{2})$