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Math Help - Showing two equations are identical.

  1. #1
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    Showing two equations are identical.

    X(t)=1/(√2) (cos(ωt))
    Y(t)=cos(ωt+φ)

    Demonstrate using trigonometry and algebra that the two equations are identical.
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  2. #2
    A Plied Mathematician
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    Those two equations are not identical. The amplitude of X is 1/(√2), whereas the amplitude of Y is 1. There's no way those two equations are identical. Is this part of a larger problem? If so, please state the original problem, word-for-word.
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  3. #3
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    Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.

    What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.

    Demonstrate using trigonometry and algebra that the two equations are identical.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by mandy9008 View Post
    Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.

    What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.


    Demonstrate using trigonometry and algebra that the two equations are identical.
    Showing two equations are identical.-waves.gif

    As Ackbeet said they cannot be equal as the have different amplitudes!. Here is an animated plot.



    In the above plot \varphi goes from -2\pi < \varphi < 2\pi
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