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

Suggested languages for you:

Americas

Europe

Q18E

Expert-verified
Found in: Page 522

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# Find a polar equation for the curve represented by the given Cartesian equation. $${\rm{4}}{{\rm{y}}^{\rm{2}}}{\rm{ = x}}$$

The substitution equation

$${\rm{r = }}\frac{{{\rm{cos\theta }}}}{{{\rm{4si}}{{\rm{n}}^{\rm{2}}}{\rm{\theta }}}}$$

See the step by step solution

## Step 1: Formulae that translate.

Formulas’ expressing a point’s Cartesian coordinates $$\left( {{\rm{x,y}}} \right)$$in terms of polar coordinates$$\left( {{\rm{r,\theta }}} \right){\rm{.}}$$

\begin{aligned}{l}{\rm{x = rcos\theta }}\\{\rm{y = rsin\theta }}\end{aligned}

## Step 2:  Replace that in the equation.

\begin{aligned}{c}{\rm{4}}{{\rm{y}}^{\rm{2}}}{\rm{ = x4 \times (rsin\theta }}{{\rm{)}}^{\rm{2}}}{\rm{ }}\\{\rm{ = rcos\theta 4}}{{\rm{r}}^{\rm{2}}}{\rm{si}}{{\rm{n}}^{\rm{2}}}{\rm{\theta }}\\{\rm{ = rcos\theta 4rsi}}{{\rm{n}}^{\rm{2}}}{\rm{\theta }}\\{\rm{ = cos\theta r }}\\{\rm{ = }}\frac{{{\rm{cos\theta }}}}{{{\rm{4si}}{{\rm{n}}^{\rm{2}}}{\rm{\theta }}}}\end{aligned}

In the equation, substitute that$${\rm{r = }}\frac{{{\rm{cos\theta }}}}{{{\rm{4si}}{{\rm{n}}^{\rm{2}}}{\rm{\theta }}}}$$