Question

How do you graph `r = 4 cos 3 theta`?

Answer 1

See graph and explanation.

Explanation:

Using

`( x, y ) = r ( cos theta, sin theta ), r = sqrt ( x^2 + y^2 )` and

`cos ntheta`

`= sum (-1)^r nC_(2r) cos^(n-2r)thetasin^(2r) theta`,

r from 0 to `[n/2]` (integer part of n/2).

the equation in Cartesian form for `r = a cos ntheta` can be obtained.

Here, n = 3 and the Cartesian equation is

#( x^2 +y^2 )^2 = 4 (x^3 - 3 x y^2),

The Socratic graph is immediate.

graph{( x^2 +y^2 )^2 - 4 (x^3 - 3 xy^2)=0[-8 8 -4 4]}