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Q. 38

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Found in: Page 583

### Precalculus Enhanced with Graphing Utilities

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

# Identify and graph each polar equation. Verify your graph using a graphing utility $r=1+\mathrm{sin}\theta$

See the step by step solution

## Step 1. Given information

$r=1+\mathrm{sin}\theta$

## Step 2. Replacing θ by -θ

$r=1+\mathrm{sin}\left(-\theta \right)\phantom{\rule{0ex}{0ex}}r=1-\mathrm{sin}\theta$

graph is symmetric with polar axis.

## Step 3. Replace θ by π-θ

Graph is symmetric with line $\theta =\frac{\pi }{2}$

## Step 4. Replace r with -r

$r=1+\mathrm{sin}\theta \phantom{\rule{0ex}{0ex}}-r=1+\mathrm{sin}\theta \phantom{\rule{0ex}{0ex}}r=-1-\mathrm{sin}\theta$

Graph may or may not be symmetric with respect to pole.