1. ## domains...

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 because sin^2theta+cos^2theta=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 in the answer(?). how do you do that?

2. Originally Posted by jeph
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 because sin^2theta+cos^2theta=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?
what are you talking about? the domain didn't change. you are mixing up domain and range

think of the sine graph. when theta is between 0 and pi, sine goes from 0 to a maximum of 1 and then back down to 0. thus the range for sin(theta) is 0<=sin(theta)<=1 when the domain is 0<=theta<=pi. but x=sin(theta), so we have 0<=x<=1

3. Originally Posted by jeph

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 in the answer(?). how do you do that?

1) the first number is 1, the second is 0
2) the first number is 0, the second is 1
3) both numbers are less than 1 but their sum is 1

so you see, each number can be 0, 1 or anything in that range, thus we get the desired domain

4. but couldnt x be -5 and y be 6 and that could equal 1 also?

5. Originally Posted by jeph
but couldnt x be -5 and y be 6 and that could equal 1 also?
wasn't there an assumption that both numbers were nonnegative? sorry, i assumed they were, i was mixing this up with the first question

Originally Posted by jeph
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 in the answer(?). how do you do that?
was this the entire question? maybe we can see why they chose that range for x if i saw the question