Chapter 9.2, Problem 2CFU

To determine

To find: the minimum and maximum value in the polar equation.

Answer to Problem 2CFU

The minimum value is $r=-2$ and maximum value is $r=8$ .

Explanation of Solution

Given information:

The polar equation is $r=3+5\sin \theta$

Calculation: since, it is known that the range of the $\sin \theta$ is $\left[-1,1\right]$ .

So the maximum value is,

  $\begin{array}{l}r=3+5\sin \theta \\ r=3+5\left(1\right)\text{ [substitute]}\\ r=8\text{ [add]}\end{array}$

And the minimum value is,

  $\begin{array}{l}r=3+5\sin \theta \\ r=3+5\left(-1\right)\text{ [substitute]}\\ r=-2\text{ [add]}\end{array}$