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Math Help - Trig problem ( i think)

  1. #1
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    Trig problem ( i think)

    what is the relationship between x and y
    if x\cos{\theta} + y\sin{\theta} = 1
    and
    x\sin{\theta} - y\cos{\theta} = 3

    [Ans: x^2 + y^2 = 10]

    Solution:

    this is my approach
    i use reverse engineering to get the correct answer (which is unacceptable):

    3^2 + 1^2 = (x\cos{\theta} + y\sin{\theta})^2 + (x\sin{\theta} - y\cos{\theta})^2

    and this is what i get
    10 = 2x^2(\cos^{2}\theta) + 2y^2(\sin^{2}\theta)
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Trig problem ( i think)

    Quote Originally Posted by TechnicianEngineer View Post
    what is the relationship between x and y
    if x\cos{\theta} + y\sin{\theta} = 1
    and
    x\sin{\theta} - y\cos{\theta} = 3

    [Ans: x^2 + y^2 = 10]

    Solution:

    this is my approach
    i use reverse engineering to get the correct answer (which is unacceptable):

    3^2 + 1^2 = (x\cos{\theta} + y\sin{\theta})^2 + (x\sin{\theta} - y\cos{\theta})^2

    and this is what i get
    10 = 2x^2(\cos^{2}\theta) + 2y^2(\sin^{2}\theta)


    3^2 + 1^2 = (x\cos{\theta} + y\sin{\theta})^2 + (x\sin{\theta} - y\cos{\theta})^2

    =x^2cos^2(t)+y^2sin^2(t)+x^2sin^2(t)+y^2cos^2(t)=

    x^2(cos^2(t)+sin^2(t))+y^2(cos^2(t)+sin^2(t))=

    x^2*1+y^2*1
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