Cotangent Function

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A Cotangent Function is a reciprocal trigonometric function of the tangent function.

[math]\cot(\theta)= \frac{b}{a}= \frac{\cos(\theta)}{\sin(\theta)}=\frac{1}{\tan(\theta)}[/math]


References

2019

  • (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Trigonometric_functions#Law_of_cotangents Retrieved:2019-4-30.
    • If : [math] \zeta = \sqrt{\frac{1}{s} (s-a)(s-b)(s-c)}\ [/math] (the radius of the inscribed circle for the triangle)

      and : [math] s = \frac{a+b+c}{2 }\ [/math] (the semi-perimeter for the triangle),

      then the following all form the law of cotangents[1] : [math] \cot{ \frac{A}{2 }} = \frac{s-a}{\zeta }\,; \qquad \cot{ \frac{B}{2 }} = \frac{s-b}{\zeta }\,; \qquad \cot{ \frac{C}{2 }} = \frac{s-c}{\zeta } [/math] It follows that : [math] \frac{\cot \dfrac{A}{2}}{s-a} = \frac{\cot \dfrac{B}{2}}{s-b} = \frac{\cot \dfrac{C}{2}}{s-c}. [/math] In words the theorem is: the cotangent of a half-angle equals the ratio of the semi-perimeter minus the opposite side to the said angle, to the inradius for the triangle.

  1. Cite error: Invalid <ref> tag; no text was provided for refs named Allen_1976


1999