Question

parametric form of r=2costheeta

Answer 1

it is already a parametric form

Answer 2

with parameter (\theta\)

Answer 3

no it is in polar form

Answer 4

if you stay in polar coordinates, you could write the parametric form as
\[ \theta= t \\ r= 2 \cos(t) \]

if you want the parametric form of this curve in rectangular coordinates, first translate from polar to rectangular coordinates, using
\[ x= r \cos(\theta) \\ y= r \sin(\theta) \\ x^2 + y^2 = r^2\]

multiply your equation by r:
\[ r^2 = 2r \cos(\theta) \\ x^2 + y^2 = 2x\\ x^2 -2x +y^2=0\]
Complete the square to get
\[ (x-1)^2 + y^2 = 1 \]
this is the equation of a circle with radius r=1 and center (1,0)
you can write it in parametric form using
\[ x= h+ r \cos(t) \\ y= k+ r \sin(t) \]
where (h,k) is the center of the circle