Question 1036384
The graph is symmetric wrt to the x-axis if {{{r(theta) = r(-theta)}}}.

Since {{{4cos(5*theta) = 4cos(-5*theta)}}}, the graph is symmetric wrt the x-axis.

The graph is symmetric wrt the y-axis if {{{r(theta) = r(pi-theta)}}}.

Since {{{4cos(5*theta) <> 4cos(5*(pi - theta)) = -4cos(5*theta) }}}, the graph is not symmetric wrt the y-axis.


The graph is symmetric wrt the y-axis if {{{r(theta) = r(pi+theta)}}}.

Since {{{4cos(5*theta) <> 4cos(5*(pi + theta)) = -4cos(5*theta) }}}, the graph is not symmetric wrt the origin.