Question

Is the polar function `5-4 sin theta` symmetric with respect to the y axis?

Answer 1

The `y` axis is the same as `theta = pi/2`. We can imagine flipping the function around the `y` axis as inserting `theta -> pi - theta`.

We know that `sin(pi-theta) = sin(theta)`, so the function is symmetric w.r.t. the `y` axis.