Chapter H.1, Problem 36E

To determine

To find: the curve with the given polar equation

Answer to Problem 36E

Thefollowing graph is drawn.

Explanation of Solution

Given:

  $r=2+\sin \theta$

Calculation:

Consider the following polar curve:

  $r=2+\sin \theta$

The objective is to sketch the curve with the given polar equation.

Find the values of r for some convenient values of $\theta$ and plot the corresponding points $\left(r,\theta \right)$ .

Compute the following table:

$\theta$	$r=2+\sin \theta$
$\pi$	$2$
$7\pi /6$	$1.5$
$5\pi /4$	$1.2929$
$4\pi /3$	$1.1340$
$3\pi /2$	$1$
$5\pi /3$	$1.1340$
$11\pi /6$	$1.5$
$7\pi /4$	$1.2929$
$2\pi$	$2$

Sketch the following graph:

  

Conclusion:

Therefore, the graph is drawn.