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
