(a) complete the table for the polar function and (b) plot the corresponding points. r = 2 cos 2θ (a) for…

Explanation:

Step1: Substitute $\theta = 0$

$r = 2\cos(2\times0)=2\cos(0)=2\times1 = 2$

Step2: Substitute $\theta=\frac{\pi}{2}$

$r = 2\cos(2\times\frac{\pi}{2})=2\cos(\pi)=2\times(- 1)=-2$

Step3: Substitute $\theta=\pi$

$r = 2\cos(2\pi)=2\times1 = 2$

Step4: Substitute $\theta=\frac{3\pi}{2}$

$r = 2\cos(2\times\frac{3\pi}{2})=2\cos(3\pi)=2\times(-1)=-2$

Step5: Substitute $\theta=\frac{7\pi}{4}$

$r = 2\cos(2\times\frac{7\pi}{4})=2\cos(\frac{7\pi}{2})=2\times0 = 0$

Answer:

$\theta$	$0$	$\frac{\pi}{4}$	$\frac{\pi}{2}$	$\frac{3\pi}{4}$	$\pi$	$\frac{5\pi}{4}$	$\frac{3\pi}{2}$	$\frac{7\pi}{4}$
$r$	$2$	$0$	$- 2$	$0$	$2$	$0$	$-2$	$0$