Typically for a circle oriented counter clockwise you use
x= rcos(t) y = rsin(t) starting at (r,0)
Here though you are moving clockwise from(0,2) so switch the sine and cosine
use x = 2sin(t)
y= 2cos(t) and let t vary from 0 to pi/4
Okay I'm having trouble parameterizing the curve C: x^2 + y^2 = 4 from (0,2) to (SQRT 2, SQRT 2) in the first quadrant in order to take the line integral for f (x,y) = x^2-y
I understand to put C into polar coordinates, and that r=2 but my key shows that r(t) = (2cost)i + (2sint)j 0<=t=<pi/2
and I have no idea how to get that r(t)...