Test the polar equation for symmetry with respect to the pol

Test the polar equation for symmetry with respect to the polar axis, and the line theta = pi/2 r =6cos theta sec theta symmetric with respwct to the polar axis symmetric with respect to the pole symmetric with respect to the line theta = pi/2 not symmetric with respect to any of these

Solution

r = 6 cos(x) csc(x)

hence, r = 6 cos(x) / sin(x)

hence, r = 6 cot(x)

r = 0 when x = pi/2

and graph of cot(x) is symmetric about x = pi/2