How do you graph #r=4costheta+4#?

Question

2184 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-30T09:33:35

For details, see explanation.

#r=a(1+cos (theta-alpha))# represents a family of cardioids,

emanating from the pole r =0.

Name reminds you of Heart symbol.

a and #alpha# are parameters

#theta = alpha# is the line of symmetry..

a gives the size of a member of this family..

Maximum r =2a, at (2a, #alpha#).

Here, in r = 4 ( 1 + cos #theta# ), a = 4 and #alpha#=0.

A short Table for graphing is given below.

#(r, theta): (0, 8) (2sqrt 2, pi/4), (2, pi/2) (0, pi)#, for upper half.that

comprises a larger part in #Q_1# and a smaller in #Q_2#.

Use symmetry about #theta = 0#, for the lower half.