Key Equations

Key Equations

Law of Sines	$\begin{array}{l}\frac{\sin \alpha }{a}=\frac{\sin \beta }{b}=\frac{\sin \gamma }{c}\hfill \\ \frac{a}{\sin \alpha }=\frac{b}{\sin \beta }=\frac{c}{\sin \gamma }\hfill \end{array}$
Area for oblique triangles	$\begin{array}{r}\hfill \text{Area}=\frac{1}{2}bc\sin \alpha \\ \hfill =\frac{1}{2}ac\sin \beta \\ \hfill =\frac{1}{2}ab\sin \gamma \end{array}$

Law of Cosines	$\begin{array}{l}{a}^2=b^2+c^2-2bc\cos \alpha \hfill \\ b^2=a^2+c^2-2ac\cos \beta \hfill \\ c^2=a^2+b^2-2abcos\gamma \hfill \end{array}$
Heron’s formula	$\begin{array}{l}\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\hfill \\ \text{where }s=\frac{(a+b+c)}{2}\hfill \end{array}$

Conversion formulas

$\begin{array}{ll}\hfill & \cos \theta =\frac{x}{r}\to x=r\cos \theta \hfill \\ \hfill & \sin \theta =\frac{y}{r}\to y=r\sin \theta \hfill \\ \hfill & r^2=x^2+y^2\hfill \\ \hfill & \tan \theta =\frac{y}{x}\hfill \end{array}$