Key Equations - Algebra and Trigonometry

Law of Sines	$\begin{array}{l} \frac{\sin α}{a} = \frac{\sin β}{b} = \frac{\sin γ}{c} \\ \frac{a}{\sin α} = \frac{b}{\sin β} = \frac{c}{\sin γ} \end{array}$
Area for oblique triangles	$\begin{array}{r} Area = \frac{1}{2} b c \sin α \\ = \frac{1}{2} a c \sin β \\ = \frac{1}{2} a b \sin γ \end{array}$

Law of Cosines	$\begin{array}{l} a^{2} = b^{2} + c^{2} - 2 b c \cos α \\ b^{2} = a^{2} + c^{2} - 2 a c \cos β \\ c^{2} = a^{2} + b^{2} - 2 a b c o s γ \end{array}$
Heron’s formula	$\begin{array}{l} Area = \sqrt{s (s - a) (s - b) (s - c)} \\ where s = \frac{(a + b + c)}{2} \end{array}$

Conversion formulas

\begin{array}{l} \cos θ = \frac{x}{r} \to x = r \cos θ \\ \sin θ = \frac{y}{r} \to y = r \sin θ \\ r^{2} = x^{2} + y^{2} \\ \tan θ = \frac{y}{x} \end{array}