Question

Test for symmetry with respect to Q=pi/2 , the polar axis and the pole.

r = 16 cos3Q

Please explain. I do not know how to do this. Thank You!!

Answer 1

if Q = pi/2 + h
r = 16 cos (3pi/2 +3h)
= 16[ cos 3pi/2 cos 3h - sin 3pi/2 sin h ]
cos 3pi/2 = 0
sin 3pi/2 = -1
so
16 sin h
is it the same for -h?
if Q = pi/2 - h
r = 16 cos (3 pi/2 -3h)
=16[ cos 3pi/2 cos 3h + sin3 pi/2 sin 3h
=16 (-sin h)
sin h is not the same as -sin h
so no, not symmetric about 3pi/2