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Thread: Derivatives of Trigonometric Functions

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    Derivatives of Trigonometric Functions

    Why is it that when we take derivatives of trig functions we also have to take the derivative of its angle? It is because we want to know how also the angle changes?
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    Re: Derivatives of Trigonometric Functions

    Please restate this question. It has no answer as written.
    Last edited by Plato; Apr 30th 2012 at 12:04 PM.
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    Re: Derivatives of Trigonometric Functions

    I believe you are referring to the "chain rule". That does not apply just to trig functions, but to any functions: if x is a function of t, x(t), then \frac{df(x)}{dt}= \frac{df}{dx}\frac{dx}{dt}.

    In particular, if the variable is an "angle" (actually, most applications of trig functions do not involve angles), \theta(t) that depends on t, the the derivative of sin(\theta(t)), with respect to t, is
    \frac{dsin(\theta)}{dt}= \frac{dsin(\theta)}{d\theta}\frac{d\theta}{dt}= cos(\theta)\frac{d\theta}{dt}.
    Last edited by HallsofIvy; Apr 30th 2012 at 12:43 PM.
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