Question

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

Answer 1

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

Explanation:

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.