Question

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

Answer 1

The graph is the circle of radius `sqrt 2` and center at `(sqrt 2, pi/4)` The pole is on the circle. The circle coordinates for the pole are `(0, -pi/4)`.

Explanation:

The given equation can be condensed to

`r=2sqrt 2 sin (theta+pi/4)`,

using `sin (theta+pi/4)`

`=sin theta cos (pi/4)+cos theta sin (pi/4)`

`=(1/sqrt 2)(sin theta+cos theta)`

Any equation of the form

`r = d cos (theta + alpha)` or

`r = d sin (theta + alpha)` represents a circle with diameter and

center at #(d/2, +-alpha).