we are doing parametric equations right now in calculus 2...but iono if i should be posting this here or in the trig forum =/

the question asks us to "eliminate the parameter to find a Cartesian equation of the curve"

x=sin(theta) , y=cos(theta) , theta is equal to or greater than 0 and equal to or less than pi

after you add and square the equation together you get x^2+y^2=1. the answer says "Since theta is equal to or greater than 0 and equal to or less than pi, we have sin(theta) equal to or greater than 0, so x is equal to or greater than 0. how did the domain change like that? why doesnt the domain just stay the same?

another question was x=sin^2(theta) , y=cos^2(theta)

x+y=1 , x equal to or greater than 0 and equal to or less than 1. the domain wasnt given in the question but it was some how calculated(?). how do you do that?