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

1 Answer
A. S. Adikesavan
May 18, 2016

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).

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