Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Answer 1

Answer:

It is symmetric about x- axis

The graph is not symmetric along the y - axis

It is not symmetric about the origin

Step-by-step explanation:

We can easily know the solution to your problem by graphing the equation

r(θ) = 2*cos (5*θ)

Please, see attached image

The graph is symmetric about the x axis if

r(θ) = r(-θ)

r(θ) = 2*cos (5*θ) = 2*cos (-5*θ) = r(-θ)

Since the cosine is an even function.

It is symmetric about x- axis

The graph is not symmetric along the y - axis, because

r(θ) ≠ r(π-θ)

It is symmetric about the origin if

r(θ)  =  r(π+θ)

But, since,

r(θ) = 2*cos (5*θ) ≠ 2*cos (5*(θ+π)) = 2*cos (5*θ+5*π)

It is not symmetric about the origin