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Math Help - Co-functions

  1. #1
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    Co-functions

    Hay all,

    So i wen't to my Lecturer to ask him about what the -x means

    in

    sin (100 + x) = cos (-x)

    And he just mumbles trying not to work as usual,

    and then he finish's saying to just skip those questions with (-x) in it,

    If you guys have Teachers that are willing to help you and mark your work, carry then on your hands,

    because once you don't have that support anymore and you have to figure out how things work and come to gether on your own,

    You'll wish for that support...

    Any help wil be much appreaciated
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  2. #2
    MHF Contributor
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    Re: Co-functions

    Hey MiloMan.

    Based on your question, the expression you are stating doesn't make sense. sin(x) != cos(-x) in general.

    If you are trying to solve for a particular x, you can use the fact that cos(-x) = cos(x) = sin(x) which means tan(x) = 1 and x = arctan(1).
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  3. #3
    MHF Contributor

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    Re: Co-functions

    Here, you have, sin(10+ x)= cos(-x). I am puzzled about you asking "what does '-x' mean". Just as in any algebra problem, it means "negative x". If x= 20 degrees then then "-x" is "negative 20 degrees".

    Now, it is true that cos(a)= sin(90- a) so that cos(-x)= sin(90- (-x))= sin(90+ x). That is, the equation is the same as sin(10+ x)= sin(90+ x). Of course, that equation would be satisfied if 10+x= 90+ x but that is impossible: subtracting x from both sides it becomes 10= 90 which is certainly NOT true! But it is also true that, for any a, sin(a)= sin(180- a) so it is also possible that 10+ x= 180- (90+ x)= 90- x. Adding x to both sides and subtracting 10 from both sides, 2x= 80, x= 40 degrees.
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