How do you test for symmetry for #r = 1 - 2sin(theta)#?

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Answer 1 · 2016-05-29T06:13:03

This is symmetrical about (y-axis) #theta=+-pi/2#.

As #cos(-theta)=cos(theta), r = f(cos(theta))# is symmetrical about (x-

axis) #theta = 0 and theta = pi#.

As #sin (pi-theta)=sin(theta), r = f(sin(theta))# is symmetrical about (y-

axis) #theta=+-pi/2#.

Here,# r = 1-2 sin (theta)=f(sin(theta).#.

If #(r, theta)# is on the curve, #(r, pi-theta)# that is equidistant (mirror

image) with respect to y-axis will also lie on the curve.