How to Find the Zeros of a Polar Graph?

To find the zeros of a polar graph, you need to identify the points where the graph intersects the origin (r = 0). Here's how you can do it:

1. Set the Equation to Zero

• Start with the polar equation that describes your graph.
• Set the equation equal to zero (r = 0).
• Solve the equation for the angle theta.

2. Finding the Values of Theta

• The solutions for theta will be the angles where the graph intersects the origin.
• These angles will be the zeros of the polar graph.

Example:

Let's say you have the polar equation r = 2cos(theta). To find the zeros, follow these steps:

1. Set the equation to zero:
   • 0 = 2cos(theta)
2. Solve for theta:
   • cos(theta) = 0
   • theta = pi/2, 3pi/2

Therefore, the zeros of the polar graph r = 2cos(theta) are at the angles theta = pi/2 and theta = 3pi/2.

Practical Insights:

• Remember that a polar graph can intersect the origin multiple times, so you might get multiple solutions for theta.
• If your equation is complex, you might need to use trigonometric identities or other algebraic techniques to solve for theta.