Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ
i don't think it's symmetric?

                The graph is symmetric about the x-axis.

Step-by-step explanation:The graph is symmetric about the polar axis(x-axis) if we replace (r,θ) with (r,-θ) then it is equivalent to the original equation.The graph is symmetric about the y-axis if we replace (r,θ) with (-r,-θ) then it is equivalent to the original equation.The graph is symmetric about the pole(origin) if we replace (r,θ) with (-r,θ) then it is equivalent to the original equation.

Here we have equation as:

           

when we replace (r,θ) with (r,-θ) we have:

(  Since, we know that:

 )

Hence, the graph is symmetric about the x-axis.

when we replace  (r,θ) with (-r,-θ)

Hence, we observe that on replacing the function the two graphs are not equivalent.

Hence, the graph is not symmetric about the y-axis.

when we replace (r,θ) with (-r,θ) we have:

Hence, we observe that on replacing the function the two graphs are not equivalent.

Hence, the graph is not symmetric about the pole(origin)