How do you find the cartesian graph of #r = 5sin(θ)#?
You basically get a circle.
Consider the following diagram:
We can see that the relationships between rectangular and polar coordinates are:
Given our expression:
so that you get, using our relationships of conversion:
which is the equation of a circle centered at
(try to substitute the values of the center and radius and you'll find (1)).
You can now plot it directly.
Next, to have some fun, I used Excel to evaluate, using our relationships of conversion, the coordinates