Q. 16. - Calculus

Question

In this section we graphed many polar equations, and

most of our examples followed similar procedures. Describe

a general procedure for sketching the graph of a

polar equation.

Step-by-Step Solution

Answer

To draw the graph take different values for $\theta$, calculate the corresponding values of $r$then plot the points $(r,\theta )$

Step 1: A polar equation's graph is a collection of points in the plane whose polar coordinates satisfy the equation.

A point in the plane is represented by the coordinate pair($(r,\theta )$ in the polar system.

Where $r$denotes the angle in radians and $\theta$indicates the distance from the pole or origin. And the positive $x$-axis is longer than the polar axis.

When $\theta >0$the angle rotates counterclockwise from the polar axis, and when$\theta <0$, the angle moves in clockwise.

The graph is made by using a positive value $\left|r\right|$

Step 2: Describe a general procedure for sketching the graph of a polar equation.

Plotting the points is one way to sketch the graph of a polar equation. We use $\theta$as the independent variable and $r$as the dependent variable when graphing a polar equation of the form $r=f\left(\theta \right)$

To make the graph, compute the equivalent values of $r$ for various $\theta$ values, then plot the points $(r,\theta )$