Question

How do you graph `r = 2 + tan(theta)`?

Answer 1

The form is r = `r_1 + r_2`, where `r_1 = 2` for a circle, with center at pole and radius = 2. `r_2 = tan theta`. Radially, `(r, theta)` is distant `tan theta`, from `(2, theta)` on the circle. .

Explanation:

The asymptotes to this 4-branch curve are `theta = pi/2` and the

opposite `theta=(3pi)/2`.

Due to infinite discontinuities at `theta = pi/2 and theta=(3pi)/2`, .the

four branches for `theta in [0, pi/2), (pi/2, pi], [pi, (3pi)/2) and ((3pi)/2, pi]` are traced in the four quadrants, in the order, ist, 3rd,

2nd and 4th. They brace the circle r =2 at (2, 0) and (2, `pi`).