Test the equation for symmetry with respect to the given axi

Test the equation for symmetry with respect to the given axis, line, or pole. r=2-2sin(theta)

Solution

r = 2-2sin(theta)

(r,-theta) implies r = 2 - 2 sin(-theta)= 2 + 2 sin(theta)

X-axis symmetry is NO since (-r, -theta) implies -r = 2 - 2 sin(theta) which implies r = -2 + 2 sin(theta)

Similarly we can find for Y- axis which is YES.