So, I encountered a question r = -|sinø|. So, I thought the polar graph would look like (2) but it actually looks like (3) and I don't understand why. Can someone explain it to me? I've attached a picture. 
2026-03-30 23:09:37.1774912177
Graphing A Polar Equation
101 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
Hint: The absolute value of a function is always greater-than-or-equal to zero, and similarly the negative of the absolute value will always be less-than-or-equal to zero.
Thus, the polar equation you posted implies that for any angle $0\le\varphi\le 2\pi$, the radial coordinate $r$ is never positive, because:
$$r{(\varphi)}=-|\sin{\varphi}|\le 0.$$
Angular coordinates in the range $0\le\varphi\le\pi$ usually correspond to the top half of the plane when the radius $r$ is positive. So, negative values of $r$ will fall in what part of the plane?
Next, consider the same questions for the case when $\pi\le\varphi\le2\pi$.