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  1. #1
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    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?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jeph View Post
    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
    Last edited by Jhevon; April 3rd 2007 at 06:07 PM.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jeph View Post

    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?
    ok, let's think about this. how can two numbers add up to be 1. well, there are three main ways:

    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
    Last edited by Jhevon; April 3rd 2007 at 09:10 PM. Reason: i was assuming here that x and y are nonnegative
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    but couldnt x be -5 and y be 6 and that could equal 1 also?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jeph View Post
    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

    Quote Originally Posted by jeph View Post
    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
    Last edited by ThePerfectHacker; April 4th 2007 at 05:55 PM.
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