For =3 cos theta - 3, r <=0=3cosθ−3,r≤0. and r is never > 0>0, for thetaθ in one
period [0. 2pi][0.2π].,
I want length r .>=0r.≥0, So, I use r = 3 - 3 cos thetar=3−3cosθ, instead.
As r is a function of cos(theta)=cos(-theta)cos(θ)=cos(−θ), the graph is
symmetrical about the axis theta = 0θ=0.
The Table for graphing this Cardioid, for one period 2pi2π, is
(r, theta): (0, 0) (3(1-sqrt3/2), pi/6) (3(1-1/sqrt2), pi/4)(r,θ):(0,0)(3(1−√32),π6)(3(1−1√2),π4)
(3/2, pi/3) (3, pi/2) (9/2, 2pi/3) (3(1+1/sqrt2), 3pi/4)(32,π3)(3,π2)(92,2π3)(3(1+1√2),3π4)
(3(1+sqrt3/2), 5pi/6) (6, pi)(3(1+√32),5π6)(6,π)
For the second half of the period [pi, 2pi],[π,2π], use symmetry( about
the axis theta = 0θ=0 to draw this half of the cardioid.
The bulge of the cardioid is far away, in the direction theta =piθ=π.
