### Home > CALC > Chapter 12 > Lesson 12.1.2 > Problem12-27

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:

1. $\operatorname{sin} θ = 0$

1. $5\operatorname{sin} θ = 4\operatorname{sin} 2θ$

1. $5\operatorname{sin} θ = 2\operatorname{sin} 2θ$

1. $5\operatorname{cos} θ = 2\operatorname{cos} 2θ$

1. $5\operatorname{cos} θ = 4\operatorname{cos} 2θ$

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.