Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 3θ

Answer 1

y-axis

Explanation:

Theta = 10

2cos(30) = sqrt(3)

Theta = -10

2cos(-30) = sqrt(3)

Theta = 180 - 10 = 170

2cos(3×170) = -sqrt(3)

Answer 2

It is symmetric about the y-axis.

Explanation:

Replace r with -r and θ with -θ.

-r = 2 cos 3(-θ)

-r = -2 cos 3θ

r = 2 cos 3θ

The same equation results so it is symmetric about the y-axis.