Overzicht goniometrie

Uit je hoofd leren:

Tabellen

 0  \frac{1}{6}\pi \frac{1}{4}\pi \frac{1}{3}\pi \frac{1}{2}\pi
sin 0 \frac{1}{2} \frac{1}{2}\sqrt{2} \frac{1}{2}\sqrt{3} 1
cos 1 \frac{1}{2}\sqrt{3} \frac{1}{2}\sqrt{2} \frac{1}{2} 0
tan 0 \frac{1}{3}\sqrt{3} 1 \sqrt{3} -
I II III IV
sin + + - -
cos + - - +
tan + - + -

Formules

-\sin(x)=\sin(-x) \sin(x)=\cos(\frac{1}{2}\pi-x) \eqalign{\tan(x)=\frac{\sin(x)}{\cos(x)}}
-\cos(x)=\cos(x-\pi) \cos(x)=\sin(\frac{1}{2}\pi-x) \sin^2(x)+\cos^2(x)=1
-\tan(x)=\tan(-x) \sin(2x)=2\sin(x)\cos(x) \cos (2x) = \left\{ \begin{array}{l} 2\cos ^2 (x) - 1 \\ 1 - 2\sin ^2 (x) \\ \cos ^2 (x) - \sin ^2 (x) \\ \end{array} \right.

Methode

\begin{array}{l} \sin (x) = \sin (A) \\ x = A + k \cdot 2\pi \vee x = \pi - A + k \cdot 2\pi \\ \end{array}
\begin{array}{l} \cos (x) = \cos (A) \\ x = A + k \cdot 2\pi \vee x = - A + k \cdot 2\pi \\ \end{array}
\begin{array}{l} \tan (x) = \tan (A) \\ x = A + k \cdot \pi \\ \end{array}

Bijzondere gevallen

\eqalign{   & \sin (x) = 0  \cr   & x = 0 + k \cdot \pi  \cr} \eqalign{   & \sin (x) = 1  \cr   & x = \frac{1} {2}\pi  + k \cdot 2\pi  \cr} \eqalign{   & \sin (x) =  - 1  \cr   & x = 1\frac{1} {2}\pi  + k \cdot 2\pi  \cr}
\eqalign{   & \cos (x) = 0  \cr   & x = \frac{1} {2}\pi  + k \cdot \pi  \cr} \eqalign{   & \cos (x) = 1  \cr   & x = 0 + k \cdot 2\pi  \cr} \eqalign{   & \cos (x) =  - 1  \cr   & x = \pi  + k \cdot 2\pi  \cr}

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