Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By SlipEternal

Thread: inverse trignometric functions in respect of Cotangent inverse

  1. #1
    Member
    Joined
    Aug 2011
    Posts
    110

    inverse trignometric functions in respect of Cotangent inverse

    Sir,

    To find the value of cot -1 (-x)
    I proceeded like this,
    Let Cot -1 (-x) = y
    -x = Cot y
    x = - Cot y = Cot ( y)
    Cot -1 x = - y = Cot -1 (-x) .

    is Cot -1 x = Cot -1 (-x).

    To find the value of cot -1 (-x)

    My friend said as follow :
    Let Cot -1 (-x) = y
    -x = Cot y
    x = - Cot y = Cot ( πy)
    Cot -1 x = π - y = π - Cot -1 (-x)
    Cot -1 x = π - Cot -1 (-x).

    Whether both the results are correct?

    Which one I have to adopt and why?

    Kindly enlighten me.

    with warm regards,

    Aranga
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,728
    Thanks
    1521

    Re: inverse trignometric functions in respect of Cotangent inverse

    Quote Originally Posted by arangu1508 View Post
    Sir,

    To find the value of cot -1 (-x)
    I proceeded like this,
    Let Cot -1 (-x) = y
    -x = Cot y
    x = - Cot y = Cot ( –y)
    Cot -1 x = - y = Cot -1 (-x) .

    is Cot -1 x = Cot -1 (-x).
    Not quite unless $y=-y=0$.

    You have $\text{Cot}^{-1} x = -y \Longrightarrow y = -\text{Cot}^{-1} x$ and $y = \text{Cot}^{-1}(-x)$. This gives you $\text{Cot}^{-1}(-x) = -\text{Cot}^{-1}x$. So, arccotangent is an odd function.

    Now, your friend's approach is not correct. This is because $\text{Cot}^{-1}$ returns a value between $-\dfrac{\pi}{2}$ and $\dfrac{\pi}{2}$. So, $\pi - y$ will yield a value outside the range of the $\text{Cot}^{-1}$ function. Note that this is different from $\cot^{-1}$. The latter is the notation used for the generic inverse of cotangent, which has an infinite number of values that satisfy it. In fact, $\cot^{-1}(-x) = n\pi - \cot^{-1}x$ is true for any integer $n$. But, for the $\text{Cot}^{-1}$ function, that is the notation for a specific value of the arccotangent expression that falls between $-\dfrac{\pi}{2}$ and $\dfrac{\pi}{2}$.

    Does that make sense?
    Thanks from arangu1508
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2011
    Posts
    110

    Re: inverse trignometric functions in respect of Cotangent inverse

    thank you it is very useful.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Aug 18th 2017, 11:48 PM
  2. Inverse cotangent on calculator.
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: Nov 15th 2010, 11:09 AM
  3. Inverse Cotangent Function
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 14th 2010, 07:55 PM
  4. Replies: 2
    Last Post: Oct 19th 2009, 03:47 AM
  5. tangent of inverse trignometric function
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Feb 4th 2007, 08:46 PM

/mathhelpforum @mathhelpforum