Question

Sketch the polar curve.

Short answer

Figure 1 shows that the polar curve is an eight-leaved rose that is symmetric around the y axis.

Step-by-step solution

Definition of Concept

Polar curve: A polar curve is a shape made with the polar coordinate system. Polar curves are defined by points that vary in distance from the origin (the pole) based on the angle measured off the positive x-axis.

Sketch the polar curve

Considering the given information:

Polar equation for the variable

Puttingthe valuefor and obtain the value of r as,

Similarly, obtain the values of and r .

Draw the polar curve for the equation using the points as shown in Figure 1.

Therefore, Figure 1 shows that the polar curve is an eight-leaved rose that is symmetric around the y axis.