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Found in: Page 523

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. $${\rm{x y = 4}}$$

The curve's polar equation is

$${{\rm{r}}^{\rm{2}}}{\rm{ = 8csc2\theta }}$$

See the step by step solution

Step 1: The curve's polar equation.

\begin{aligned}{l}{\rm{x = rcos\theta ,}}\;\;\;{\rm{y = rsin\theta }}\\{\rm{xy = 4(rcos\theta )(rsin\theta ) = 4}}\\{{\rm{r}}^{\rm{2}}}{\rm{cos\theta sin\theta = 4}}\\{{\rm{r}}^{\rm{2}}}{\rm{ = }}\frac{{\rm{4}}}{{{\rm{cos\theta sin\theta }}}}\\{{\rm{r}}^{\rm{2}}}{\rm{ = }}\frac{{\rm{8}}}{{{\rm{sin2\theta }}}}\end{aligned}

Step 2: As a result, the curve's polar equation is.

It's important to understand that r is not the same as radius; it's simply a parameter that can take any actual value.

$${{\rm{r}}^{\rm{2}}}{\rm{ = 8csc2\theta }}$$