Chapter 8, Problem 3RCC

To determine

To sketch: the graph of a polar equation $r=f\left(\theta \right)$ .

Answer to Problem 3RCC

The procedure of sketching the curve of a polar equation $r=f\left(\theta \right)$ is explained.

Explanation of Solution

Calculation:

Explain the procedure to sketch the graph of a polar equation $r=f\left(\theta \right)$ .

The graph of polar equations $r=f\left(\theta \right)$ consists of all point P that has at least one polar representation $\left(r,\theta \right)$ where coordinates satisfy the equation.

First determine the polar coordinates of several points on the curve by putting different values of in the equation $r=f\left(\theta \right)$ and the corresponding values of r.

The results are then shown in a table which consists of two rows and several columns.

First row is for $\text{'}\theta \text{'}$ and second row is for $\text{'}r=f\left(\theta \right)\text{'}$ .

Plot these points in polar coordinates and then join those points to sketch the curve.

Thus, the curve of a polar equation $r=f\left(\theta \right)$ is sketched.

Conclusion:

Therefore, the procedure of sketching the curve of a polar equation $r=f\left(\theta \right)$ is explained.