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Q. 43

Expert-verified
Found in: Page 567

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.$\left(6,150°\right)$

The rectangular coordinates corresponding to the polar coordinates $\left(6,150°\right)$are$\left(-3\sqrt{3},3\right)$

See the step by step solution

## Step 1. Given information

The given poplar coordinates of a point $\left(6,150°\right)$

## Step 2. Finding the value of x

For a point P on the terminal side of $\theta$ and having polar coordinates $\left(r,\theta \right)$ , the corresponding rectangular coordinates are given by $x=r\mathrm{cos}\theta$and $y=r\mathrm{sin}\theta$ .
Substitute $6$ for $r$ and $150°$ for $\theta$ in to get the value of x .

$x=r\mathrm{cos}\theta \phantom{\rule{0ex}{0ex}}=6.\mathrm{cos}\left(150°\right)\phantom{\rule{0ex}{0ex}}=6.\left(-\frac{\sqrt{3}}{2}\right)\phantom{\rule{0ex}{0ex}}=-3\sqrt{3}$

## Step 3. Find the value of y.

$y=r\mathrm{sin}\theta \phantom{\rule{0ex}{0ex}}=6.\mathrm{sin}\left(150°\right)\phantom{\rule{0ex}{0ex}}=6.\frac{1}{2}\phantom{\rule{0ex}{0ex}}=3$

Therefore, the rectangular coordinates corresponding to the polar coordinates $\left(6,150°\right)$are $\left(-3\sqrt{3},3\right)$