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Math Help - Trig ratios

  1. #1
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    Trig ratios

    Hi forum,

    I've got a question - What is tan^-1(cot(x))? My calculator gives me a senseless answer.

    Thanks.
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  2. #2
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    Re: Trig ratios

    Quote Originally Posted by qwertyuiop View Post
    Hi forum,

    I've got a question - What is tan^-1(cot(x))? My calculator gives me a senseless answer.

    Thanks.
    1. Go back to the basics. Use a right triangle (see attachment)

    2. \tan(A)=\frac ab~\implies~\tan^{-1}\left(\frac ab\right) = A

    3. \angle(A)+\angle(B)=\frac \pi2

    4. \cot(A)=\frac ba = \tan(B)

    5. ... and now you are able to determine \tan^{-1}(\cot(A))
    Attached Thumbnails Attached Thumbnails Trig ratios-tancotrelat.png  
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  3. #3
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    Re: Trig ratios

    Ok... I see... kinda...

    x=tan^-1(cot(x))
    x=tan^-2(tan(pi/2-x))
    x=pi-x

    Yes?
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  4. #4
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    Re: Trig ratios

    Quote Originally Posted by qwertyuiop View Post
    ... What is tan^-1(cot(x))?
    Quote Originally Posted by qwertyuiop View Post
    Ok... I see... kinda...

    x=tan^-1(cot(x))
    ...
    No.

    That's completely different from your original question!

    You only can state that

    \tan^{-1}\left(\cot(x) \right) = \frac \pi2 - x
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  5. #5
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    Re: Trig ratios

    Sorry, that's what i meant

    Thank you!
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