CPM Homework Help : CALC Problem 12-27

Multiple Choice: At the points where the limaςon $r = 5 − 4\operatorname{cos} θ$ has a horizontal tangent, the following equation is true:

$\operatorname{sin} θ = 0$

$5\operatorname{sin} θ = 4\operatorname{sin} 2θ$

$5\operatorname{sin} θ = 2\operatorname{sin} 2θ$

$5\operatorname{cos} θ = 2\operatorname{cos} 2θ$

$5\operatorname{cos} θ = 4\operatorname{cos} 2θ$

Hint:

This is when $\frac{dy}{dθ} = 0$ .
$y = r\sin(\theta)=(5-4\cos(\theta))\sin(\theta)$
You will need to use a double angle identity to rewrite your $y =$ equation or your final answer.