fill in the blank. the equation r² = 4 sin(2θ) represents a --select-- need help? read it
fill in the blank. the equation r² = 4 sin(2θ) represents a --select-- need help? read it
Answer
Explanation:
Step1: Recall polar - curve equations
The general form of a polar - curve is (r = f(\theta)). The given equation is (r^{2}=4\sin(2\theta)), or (r = \pm2\sqrt{\sin(2\theta)}). The equation (r^{2}=a^{2}\sin(2\theta)) is a well - known form of a lemniscate.
Step2: Identify the curve type
When we have an equation of the form (r^{2}=a^{2}\sin(2\theta)) (in our case (a = 2)), the curve represented in polar coordinates is a lemniscate.
Answer:
lemniscate