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

r = 2 + 3 sin θ

choices:
no symmetry
y-axis only
x-axis only
origin only

Step-by-step explanation:

The given equation is

Notice that this equation is in polar form.

If can be replace with or , then the graph is symmetric to the line , which is a vertical line.

Let's evaluate the given equation.

But,

So,  

Notice that the change produces the same equation.

Therefore, the given polar expression is symmetric to , which is the y-axis only in the coordinate system.

So, the right answer is y-axis only.

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

7

step-by-step explanation:

the answer would be 7