Chapter 9, Problem 1RE

To determine

To plot:the given points in the polar coordinates and find the rectangular coordinates.

Answer to Problem 1RE

  ${\left(3,\frac{\pi }{6}\right)}_{r\theta }={\left(\frac{3\sqrt{3}}{2},\frac{3}{2}\right)}_{xy}$ .

Explanation of Solution

Given:

The givenpint is $\left(3,\frac{\pi }{6}\right)$ .

Calculation:

As it is known that $x=r\cos \theta y=r\sin \theta$ .

And the given pint is $\left(3,\frac{\pi }{6}\right)$ .

Therefore,

  $\begin{array}{l}x=3\cos \frac{\pi }{6}=3\left(\frac{\sqrt{3}}{2}\right)=\frac{3\sqrt{3}}{2}\\ y=3\sin \frac{\pi }{6}=3\left(\frac{1}{2}\right)=\frac{3}{2}\\ \therefore {\left(3,\frac{\pi }{6}\right)}_{r\theta }={\left(\frac{3\sqrt{3}}{2},\frac{3}{2}\right)}_{xy}\end{array}$

Hence, the rectangular coordinates of the given point is ${\left(3,\frac{\pi }{6}\right)}_{r\theta }={\left(\frac{3\sqrt{3}}{2},\frac{3}{2}\right)}_{xy}$ .