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Math Help - Graphing Trigonometric Functions and computing their derivative

  1. #1
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    Graphing Trigonometric Functions and computing their derivative

    For an upcoming midterm, I need to be able to do the following: graph, indicate direction & speed, compute the derivative, and find critical points of trigonometric and hyperbolic functions.

    For example:

    (sin\theta, cos\theta)

    (csc\theta, cot\theta) \theta \neq k\pi, k\in Z

    (cosh t, sinh t)

    What perplexes me is the form: (a, x) with respect to theta. Are these parametric plots or the two functions mapped onto one plot? My interpretation is that they are parametric. So, for example,

    (sin\theta, cos\theta)

    Should be a unit circle except  sin\theta = x and cos\theta = y

    If this is true, do I take the derivative of  sin\theta = x => cos\theta and cos\theta = y => -sin\theta?

    But then the plot of its derivative is also graphically the same as the original function. Any help would be greatly appreciated, thanks for your time.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Yuma, AZ, USA
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    If you are correct that

    (\cos(\theta),\sin(\theta)) is parametric then to find the derivative you can use this formula

    if
    x=\cos(\theta);y=\sin(\theta)
    Then
    \displaystyle \frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{  d\theta}}=\frac{\cos(\theta)}{-\sin(\theta)}
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