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Q54.

Expert-verifiedFound in: Page 593

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Polar Equations to Rectangular Equations **

**Convert the polar equation to rectangular coordinates **

**$\theta =\pi $**

The rectangular equation is$y=0$

An equation is given in polar coordinate system as$\theta =\pi $

Use formulas and replace the value in them to convert to a rectangular coordinate system. Simplify them, and you'll get the solution. In the rectangukar coordinate system, it will provide a curve.

Formulae used,

$\theta ={\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)$

Substitute the values in the formulae,

$\begin{array}{l}\Rightarrow \theta =\pi \\ \Rightarrow \mathrm{tan}\theta =\mathrm{tan}\pi \\ \Rightarrow \frac{y}{x}=\\ \Rightarrow y=0\end{array}$

It is x axis

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