Cartesian equation for the curve?

Question

Identify curve by finding a cartesian equation for the curve:

r=csc(theta)

I know that csc=1/sin and csc=r/y. But I think it involves some sort of trigonomic trick in order to complete the problem. Any help is greatly appreciated!

Answer 1

Once you have the polar coordinates r and theta, the Cartesian elements are:

x = r cos(theta)
y = r sin(theta)

So then we can write
x = csc(theta) cos(theta) = cos(theta) / sin(theta) = tan(theta)
and
y = csc(theta) sin(theta) = sin(theta) / sin(theta) = 1

Which mean that we have a line at y = 1.

Answer 2

r=1/sin t
so rsint =1 and as rsin t =y the equation is y=1