Formeln für Winkelfunktionen

Formeln für das Rechnen mit Winkelfunktionen.

Grundformeln

$$\begin{array}{rcl}{\sin }^2(x)+{\cos }^2(x)& =& 1\\ \tan (x)\cdot \cot (x)& =& 1\\ \sin (x)& =& \cos (x-\frac{\pi }{2})\\ \cos (x)& =& \sin (x+\frac{\pi }{2})\\ \cot (x)& =& \tan (-x+\frac{\pi }{2})\end{array}$$

Darstellung von Tangens und Kotangens

$$\begin{array}{rcl}\tan (x)& =& \frac{\sin (x)}{\cos (x)}\\ \cot (x)& =& \frac{\cos (x)}{\sin (x)}\end{array}$$

Funktionen mit dem Argument 2x und x/2

$$\begin{array}{rcl}\sin (2x)& =& 2\sin (x)\cos (x)\\ \cos (2x)& =& {\cos }^2(x)-{\sin }^2(x)\\ |\sin (\frac{x}{2})|& =& \sqrt{\frac{1-\cos (x)}{2}}\\ |\cos (\frac{x}{2})|& =& \sqrt{\frac{1+\cos (x)}{2}}\end{array}$$

Additionstheoreme

$$\begin{array}{rcl}\sin (x+y)& =& \sin (x)\cos (y)+\cos (x)\sin (y)\\ \sin (x-y)& =& \sin (x)\cos (y)-\cos (x)\sin (y)\\ \cos (x+y)& =& \cos (x)\cos (y)-\sin (x)\sin (y)\\ \cos (x-y)& =& \cos (x)\cos (y)+\sin (x)\sin (y)\end{array}$$