Question

what is the name of the shape graphed by the function theta= 5pi/3
(a) Limacon with inner loop
(b) spiral
(c)circle
(d) line

Answer 1

In all but one of those, to draw it on a piece of paper you have to adjust your angle.

Answer 2

how do I do that?

Answer 3

You can do this to check. Just plot the function.
Plot the points where the angle is constant on the polar plane.

Answer 4

but 5pi/3 is the only thing given

Answer 5

When you have a constant angle like the given 5pi/3 you get a line on the polar plane

You can also get an idea by moving back to the cartesian plane
Assume theta is given
theta = tan(y/x)
arctan(theta)=y/x
y=arctan(theta)*x ===> a line