Calculus problem: Find all points of horizontal tangency. (Round your answers to four decimal places.)

Question

r = 6 sin 𝜃 cos² 𝜃      0 ≤ 𝜃 < 2𝜋

Find all points of horizontal tangency. (Round your answers to four decimal places.)

(r, 𝜃) = (0, 0) (Smallest 𝜃-value)

(r, 𝜃) = ?

(r, 𝜃) = ? (Largest 𝜃-value)

Answer 1

A student stumbled on this question posted years ago and asked if I could provide an explanation.

Here is the Desmos graph used in the video answer:

desmos.com/calculator/dky1ktuse5