Question

How do you graph `r=4sintheta`?

Answer 1

Graph of this circle through the pole r = 0, with radius 2 and center at (2, 1.57), nearly, is inserted

Explanation:

The equation `r=2a cos (theta-alpha)` represents the family of

circles through the pole r = 0 and having center on `theta=alpha` at

`(a, alpha)`.

Here, `a = 2 and alpha =pi/2` and the center is at `(1, pi/2)`.

In cartesian form,

`r = sqrt(x^2+y^2)=4 sin theta = 4(y/r)=4(y/sqrt(x^2+y^2))`

Graph for this is inserted.

graph{(x^2+y^2)-4x=0 [-5.64, 5.64, -2.82, 2.82]}