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Math Help - Solving a Trigonometric Equation

  1. #1
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    Solving a Trigonometric Equation

    Solve for x:
    cos (x) = 3x/(2pi)

    The asnwer is pi /3 but how is it solved algebraically???
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  2. #2
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    I don't think this can be solved algebraically...
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  3. #3
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    ok. Then how can I prove that pi/3 is the answer?
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  4. #4
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    LHS = cos(pi/3) = 1/2


    RHS = 3(pi/3)/(2pi) = pi/(2pi) = 1/2 = LHS.


    So x = pi/3 is a solution.
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  5. #5
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    Yes x = pi/3 is a solution.
    But how is x = pi/3 derived in the first place???




    Quote Originally Posted by Prove It View Post
    LHS = cos(pi/3) = 1/2


    RHS = 3(pi/3)/(2pi) = pi/(2pi) = 1/2 = LHS.


    So x = pi/3 is a solution.
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  6. #6
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    Quote Originally Posted by bakchormee View Post
    Yes x = pi/3 is a solution.
    But how is x = pi/3 derived in the first place???
    Probably from examining the point of intersection of the graphs of y = cos(x) and y = 3x/(2pi), or using numerical methods.
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  7. #7
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    What do you mean by numerical methods?

    Yes by graphing it, the point of intersection if x = pi/3.
    But i need to know it is derived...?
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  8. #8
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    Quote Originally Posted by bakchormee View Post
    What do you mean by numerical methods?

    Yes by graphing it, the point of intersection if x = pi/3.
    But i need to know it is derived...?
    Numerical methods are iterative methods, such as the Bisection Method or Newton's Method. Google them.

    Like I said, this point of intersection can NOT be solved algebraically, because you have a trigonometric function on one side and a polynomial function on the other. There is no way to combine them...
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  9. #9
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    Thanks for that.
    I having problems deriving x to show the prove though.....
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