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Expert-verified Found in: Page 593 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Polar Coordinates to Rectangular Coordinates Find the rectangular coordinates for the point whose polar coordinates are given.$\left(4,\pi /6\right)$

The rectangular coordinates of the point $\left(4,\frac{\pi }{6}\right)$ are.${\left(2\sqrt{3},2\right)}^{.}$

See the step by step solution

## Step 1.Given information.

The polar coordinates of the point are$\left(4,\frac{\pi }{6}\right)$ .

## Step 2. We can find the rectangular coordinates of the point using the polar to rectangular coordinates conversion formulas.

Since the polar coordinates are $\left(4,\frac{\pi }{6}\right)$ , we can say that $r=4$ and

$\begin{array}{l}\theta =\frac{\pi }{6}\\ ⇒x=r\mathrm{cos}\theta \\ ⇒x=4\mathrm{cos}\left(\frac{\pi }{6}\right)\\ ⇒x=4\cdot \left(\frac{\sqrt{3}}{2}\right)\\ ⇒x=2\sqrt{3}\end{array}$

Now, to find the value of y,

$\begin{array}{l}⇒y=r\mathrm{sin}\theta \\ ⇒y=4\mathrm{sin}\left(\frac{\pi }{6}\right)\\ ⇒y=4\cdot \left(\frac{1}{2}\right)\\ ⇒y=2\end{array}$ ### Want to see more solutions like these? 