Me! i need a better explanation!
graph the lamniscate curve r^2 = 4cos2feta
my professor told me to derive it, but i don't know what he's taking about.

1) Those are polar coordinates

2) The expression inside cosine is the angle of the vector to be drawn

3) r is the length of the vector to be drawn.

For example:

- if you take angle =0 and r results to be =2, it means that you have to put a point over the x-axis at a distance of two units from the origin.

4) You have to look for notable values, like points on the axis and notable angles (0, 45°, 90°, 180 °,...)

5) Use derivation to find maximum and minimum values. 

6) The graph of this function looks like the infinite symbol: ∞

7) Some notable points are: (0,0) ; (0,2) ; (0, - 2)

See attached the complete graph as a reference.