# Fundamental Mathematics/Trigonometry/Trignometry Function

## Trignometry Function

Relation of right triangle sides are defined as trigonometry functions. They are

 Trignometry Function Definition Mathematical Formula Graphs Sin Opposite side over hypotnuse ${\displaystyle \sin A={\frac {a}{h}}}$ Cos Adjacent side over hypotnuse ${\displaystyle \cos A={\frac {b}{h}}}$ Tang Opposite over Adjacent ${\displaystyle \tan A={\frac {a}{b}}}$ Cotang Adjacent over opposite ${\displaystyle \cot A={\frac {b}{a}}}$ Sec 1 over opposite ${\displaystyle \sec A={\frac {h}{b}}}$ Cosec 1 over adjacent ${\displaystyle \csc A={\frac {h}{a}}}$

## The Sin function

Trignometry

${\displaystyle Sin\theta =Cos(\theta -{\frac {\pi }{2}})}$

Calculus

${\displaystyle Sin\theta =-{\frac {d}{d\theta }}Cos\theta }$

Eucleur's complex circle

${\displaystyle f(\theta )=Sin\theta ={\frac {Z(\theta )-Z^{*}(\theta )}{2j}}}$

In solving wave equation of the form ${\displaystyle f^{''}(t)=-\omega f(t)}$ gives Sin function as a wave function

${\displaystyle f(t)=ASin\omega t}$

From above, when ${\displaystyle ASin\omega t=ASin\theta }$

${\displaystyle \omega t=\theta }$