Chapter 8.2, Problem 49E

To determine

To match the below equation with the graph labeled I-IV where

  $r=\sin \theta /2$

  

Answer to Problem 49E

The graph that matches the equation $r=\sin \theta /2$ is IV

  

  $\begin{array}{l}\theta =0,r=0\\ \theta =\pi ,r=1\\ \theta =\pi /2,r=0.7\\ \theta =2\pi ,r=0\end{array}$

Explanation of Solution

Given: Polar equation: $r=\sin \theta /2$

Formula Used:

A polar equation is any equation that describes a relation between r and θ , where r represents the distance from the pole (origin) to a point on a curve, and θ represents the counter-clockwise angle made by a point on a curve, the pole, and the positive x-axis.

After plotting the points in the graph it can be seen that $r=\sin \theta /2$ gives the below graph and matches with the label IV graph

Calculation:

When

  $\begin{array}{l}\\ \theta =\pi ,r=1\\ \theta =\pi /2,r=0.7\\ \theta =2\pi ,r=0\end{array}$

Conclusion:

Hence the graph labelled IV matches the given equation $r=\sin \theta /2$