Question

I got c.! Describe the graph of y=6sintheta

a. A circle of radius 3 with center at the point (3, 90°)
b. A circle of radius 6 with center at the point (6, 90°)
c. A circle of radius 3 with center at the point (3, 0°)
d. A circle of radius 6 with center at the point (6, 0°)

Answer 1

I assume this is a polar equation and it was meant to be put into the form r = 6sinθ. If not, then I might be completely wrong here :P

With these polar graphs, what I always do is make a little chart, that way I can graph it and visualize it better.
Start at θ = 0, and work your way around to 2π:

r = 6sinθ
θ r
π/4 3√2
π/2 6
3π/4 3√2
π 0
5π/4 -3√2
3π/2 -6
7π/8 -3√2
2π 0

You'll notice here that when the angle goes beyond π, the radius is negative and therefore the curve loops back around upon itself, making two complete revolutions in one 360° (2π) rotation.
So your polar graph looks something like this as you go around the circle:

As you can see, that is a circle with diameter of 6 (radius of 3) and is centered on the point (0, 3) in (x, y) format.
(0, 3) is the same thing as (3, π/2) in polar form or in your case, (3, 90°).