Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ


Asked by maham237 @ in Mathematics viewed by 384 People


r = 2 cos 5θ How do we know? Can you share the explanation/steps?

Answered by maham237 @



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


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