test for symmetry and graph the polar equation. r² = 4 cos(2θ) a. is the polar equation symmetrical with…

test for symmetry and graph the polar equation. r² = 4 cos(2θ) a. is the polar equation symmetrical with respect to the polar axis? a. the polar equation failed the test for symmetry which means that the graph may or may not be symmetric with respect to the polar axis. b. yes. c. the polar equation failed the test for symmetry which means that the graph is not symmetric with respect to the polar axis.

test for symmetry and graph the polar equation. r² = 4 cos(2θ) a. is the polar equation symmetrical with respect to the polar axis? a. the polar equation failed the test for symmetry which means that the graph may or may not be symmetric with respect to the polar axis. b. yes. c. the polar equation failed the test for symmetry which means that the graph is not symmetric with respect to the polar axis.

Answer

Explanation:

Step1: Recall polar - axis symmetry test

Replace $\theta$ with $-\theta$ in the polar equation $r^{2}=4\cos(2\theta)$.

Step2: Evaluate $\cos(-2\theta)$

We know that $\cos(-x)=\cos(x)$ for any real - number $x$. So, when we replace $\theta$ with $-\theta$ in $r^{2}=4\cos(2\theta)$, we get $r^{2}=4\cos(- 2\theta)=4\cos(2\theta)$. Since the equation remains the same after replacing $\theta$ with $-\theta$, the graph of the polar equation is symmetric about the polar axis.

Answer:

B. Yes.