• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

### Select your language

Suggested languages for you:

Americas

Europe

Q 42.

Expert-verified
Found in: Page 731

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.${r}^{2}=\mathrm{sin}\theta$

The required equation is ${\left({x}^{2}+{y}^{2}\right)}^{\frac{3}{2}}=y$.

See the step by step solution

## Step 1. Given information.

The given equation in polar coordinates is:

${r}^{2}=\mathrm{sin}\theta$

## Step 2. Find the equation in rectangular coordinates.

${r}^{2}=\mathrm{sin}\theta$

First, multiply both sides by r,

$r·{r}^{2}=r\mathrm{sin}\theta \phantom{\rule{0ex}{0ex}}{r}^{3}=y\left[r\mathrm{sin}\theta =y\right]\phantom{\rule{0ex}{0ex}}{\left(\sqrt{{x}^{2}+{y}^{2}}\right)}^{3}=y\left[{r}^{2}={x}^{2}+{y}^{2}\mathrm{and}r=\sqrt{{x}^{2}+{y}^{2}}\right]\phantom{\rule{0ex}{0ex}}{\left({x}^{2}+{y}^{2}\right)}^{\frac{3}{2}}=y$

Therefore, the equation in rectangular coordinates is ${\left({x}^{2}+{y}^{2}\right)}^{\frac{3}{2}}=y$.