Chapter 9.5, Problem 32E

To determine

To calculate: To find the rectangular coordinates of the point given in polar coordinates

Answer to Problem 32E

The rectangular coordinate of point is $\left(-3.77,3.73\right)$

Explanation of Solution

Given information: Point in polar coordinates is $\left(-5.3,-0.78\right)$

Formula Used:

Polar coordinate is given as $\left(r,\theta \right)$ , where $r$ is radius of circle

Rectangular coordinate of the point in polar coordinate $\left(r,\theta \right)$ is given as

  $x=r\cos \theta$

  $y=r\sin \theta$

Calculation:

Point in polar coordinates is given as

  $\left(-5.3,-0.78\right)$

Rectangular coordinate of the point is calculated as follows:

  $x=r\cos \theta$ and

  $y=r\sin \theta$

Calculating x coordinate,

  $\begin{array}{l}x=-5.3\cos \left(-0.78\right)\\ x=-3.77\end{array}$

Now, calculating y coordinate

  $\begin{array}{l}y=-5.3\sin \left(-0.78\right)\\ y=3.73\end{array}$

Thus, rectangular coordinate is $\left(-3.77,3.73\right)$

Conclusion:

Hence, the rectangular coordinate of point is $\left(-3.77,3.73\right)$