graph r=4sin3theta?

Answer 1

You absolutely, positively cannot subtract off 2θ.

I can't show the graph here but I can describe it. It is a "flower" with three petals all of which start and end at the origin. It reaches a maximum radius of 4 at θ = π/6, a minimum radius of -4 at θ = π/2, and a maximum of 4 at 5π/6. Then it repeats the cycle.

The minimum of -4 at θ = π/2 looks like a maximum of 4 at 3π/2.

Answer 2

first, you can subtract 2 theta off of the 3 theta, as 2 theta is a complete circuit around the circle. This leaves you with:

r=4sintheta

Now, the easiest way to do this is to put pi/2 in for theta and solve. Why? because the sin pi/2 = 1. Then, 1x4 =4

So, r=4. This means you can draw a circle with a radius of 4 originating from the origin.