Chapter 6.4, Problem 18E

Solution

To find: The rectangular coordinates with the given polar coordinates.

The rectangular coordinate is $\left(1.62,1.18\right)$ .

Given data:

The polar coordinate is $\left(-2,\frac{-14\pi }{5}\right)$ .

Formula used:

The rectangular coordinate of the polar coordinate $\left(r,\theta \right)$ is given by,

  $\begin{array}{c}x=r\cos \theta \\ y=r\sin \theta \end{array}$

Calculation:

Substitute $-2$ for $r$, and $\frac{-14\pi }{5}$ for $\theta$ in $x=r\cos \theta$ .

  $\begin{array}{c}x=-2\cos \left(\frac{-14\pi }{5}\right)\\ \approx 1.62\end{array}$

Substitute $-2$ for $r$, and $\frac{-14\pi }{5}$ for $\theta$ in $y=r\sin \theta$ .

  $\begin{array}{c}y=-2\sin \left(\frac{-14\pi }{5}\right)\\ \approx 1.18\end{array}$

Therefore, the rectangular coordinate is $\left(1.62,1.18\right)$ .