Basic trigonometry¶
For a right angle triangel we have:
\[
\sin \theta = \frac{opposite}{hypotenuse}
\]
\[
\cos \theta = \frac{adjacent}{hypotenuse}
\]
\[\begin{split}
\tan \theta = \frac{opposite}{adjacent} \\
\tan \theta = \frac{\sin \theta}{\cos \theta}
\end{split}\]
Soh-Cah-Toa
Radians¶
\(\pi \text{radian} = 180^o\)
Law of sine¶
For any triangle this holds
\[
\frac{\sin \alpha}{a} = \frac{\cos \beta}{b} = \frac{\sin \gamma}{c}
\]
Law of cosine¶
\[
c^2 = a^2 + b^2 - 2ab \cos \gamma
\]
Identities¶
\[\begin{split}
\sin(-\theta) = - \sin(\theta) \\
\cos(-\theta) = \cos(\theta) \\
\sin 2 \theta = 2\sin \theta \\
\cos 2 \theta = \cos^2 \theta - \sin^2 \theta = 2\cos^2 \theta - 1 = 1 - \sin^2 \theta \\
\sin(\theta \plusmn \pi) = \sin \theta \cos \phi \plusmn \cos \theta \sin \phi \\
\cos(\theta \plusmn \pi) = \cos\theta \cos \phi -+ \sin \theta \sin \phi
\end{split}\]