SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 5θ

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 5θ      Log On


   

Question 1036384: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 cos 5θ
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The graph is symmetric wrt to the x-axis if r%28theta%29+=+r%28-theta%29.
Since 4cos%285%2Atheta%29+=+4cos%28-5%2Atheta%29, the graph is symmetric wrt the x-axis.
The graph is symmetric wrt the y-axis if r%28theta%29+=+r%28pi-theta%29.
Since 4cos%285%2Atheta%29+%3C%3E+4cos%285%2A%28pi+-+theta%29%29+=+-4cos%285%2Atheta%29+, the graph is not symmetric wrt the y-axis.

The graph is symmetric wrt the y-axis if r%28theta%29+=+r%28pi%2Btheta%29.
Since 4cos%285%2Atheta%29+%3C%3E+4cos%285%2A%28pi+%2B+theta%29%29+=+-4cos%285%2Atheta%29+, the graph is not symmetric wrt the origin.