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Thread: Usage of cotg; Area of polygon

  1. #1
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    Thumbs up Usage of cotg; Area of polygon

    Hi Forum
    Here is a question

    $\displaystyle A=[ns^2 cotg (\pi/n)]/4$

    I am confused about the usage of cotg in this formula. How was this formula calculated?

    If we use only tg we'd get
    $\displaystyle na^2tan(\pi/n)$

    This $\displaystyle \pi/n$ angle regards the angle of the side $\displaystyle s$, correct?

    I'm no pro in co-trigonometric functions but,
    Will this, in any way, relate to the fundamental propriety of cotg=A/O?
    Trigonometric functions on non right angles are rather strange.

    Thanks.
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  2. #2
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    Re: Usage of cotg; Area of polygon

    Quote Originally Posted by Zellator View Post
    Hi Forum
    Here is a question

    $\displaystyle A=[ns^2 cotg (\pi/n)]/4$
    I am confused about the usage of cotg in this formula. How was this formula calculated?

    If we use only tg we'd get
    $\displaystyle na^2tan(\pi/n)$

    This $\displaystyle \pi/n$ angle regards the angle of the side $\displaystyle s$, correct?
    No that is not correct.
    $\displaystyle \Theta = \frac{{2\pi }}{n}$ is the central angle of a regular polygon.
    Thus we have $\displaystyle \cot (\Theta ) = \frac{{2a}}{s}$.
    Note that $\displaystyle a$ is the length of the altitude and $\displaystyle s$ is the length of the base.
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  3. #3
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    Thumbs up Re: Usage of cotg; Area of polygon

    Quote Originally Posted by Plato View Post
    $\displaystyle \Theta = \frac{{2\pi }}{n}$ is the central angle of a regular polygon.
    Thus we have $\displaystyle \cot (\Theta ) = \frac{{2a}}{s}$.
    Note that $\displaystyle a$ is the length of the altitude and $\displaystyle s$ is the length of the base.
    Hi Plato
    I guess I didn't know how to put the central angle part in proper terms. Thanks for the explanation.
    Though I'm kind of confused of where does the 2 in $\displaystyle a$ comes from.

    Maybe we have a two there because $\displaystyle s$ is actually $\displaystyle \frac{{s}}{2}$?

    Ok this was very confusing before your explanation.
    I hope I got it right!
    Thanks again Plato!
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