Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Answer 1

Hello,

Answer B: y-axis only
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Answer 2

Answer:

y-axis only.

Step-by-step explanation:

The given equation is

$r=2+3sin \theta$

Notice that this equation is in polar form.

If $(r, \theta)$ can be replace with $(r, \pi - \theta)$ or $(-r, -\theta)$, then the graph is symmetric to the line $\theta = \frac{\pi}{2}$, which is a vertical line.

Let's evaluate the given equation.

$r=2+3sin \theta=2+3sin(\pi -\theta)= 2-3sin(- \theta)$

But, $sin(-\theta)=-sin \theta$

So,  $r= 2-3sin(- \theta)=2-(-3sin\theta)=2+3sin\theta=r$

Notice that the change produces the same equation.

Therefore, the given polar expression is symmetric to $\theta = \frac{\pi}{2}$, which is the y-axis only in the coordinate system.

So, the right answer is y-axis only.