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Thread: Inverse reciprocal trig functions

  1. #1
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    Question Inverse reciprocal trig functions

    Hi,

    I hope someone can help. Can someone please explain to me why sec^1(x) does NOT equal 1/cos^1(x) and why sec^1(x) does equal cos^1(1/x)?

    The notation can get a bit confusing.

    Thanks,
    Olivia
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  2. #2
    Junior Member Ahri's Avatar
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    Re: Inverse reciprocal trig functions

    Do you know how to find the inverse of a function $f(x)$?

    Write $$f(x) = \frac{1}{\cos(x)}=y$$

    Interchange the $x$ and $y$ to get

    $$\frac{1}{\cos(y)}=x$$

    Isolate $y$,

    $$\cos(y)= \frac{1}{x}$$
    $$y= \cos^{-1} \left(\frac{1}{x}\right)$$

    Which is $f^{-1}(x)$.
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  3. #3
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    Re: Inverse reciprocal trig functions

    Okay yeah I understand that. Thank you
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