trigonometry

$$\frac{\sin(\text{A})}{\text{a}} = \frac{\sin(\text{B})}{\text{b}} = \frac{\sin(\text{C})}{\text{c}}$$

$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$

$$\small (\cos x+ i \sin x)^n=\cos(nx)+i\sin(nx)$$

$$\sin(2\theta) = 2 \cdot \sin(\theta) \cdot \cos(\theta)$$

$$\scriptsize \sin(a \pm b) = \sin(a) \cos(b) \pm \cos(a) \sin(b)$$

$$\sinh(x) = \frac{e^x - e^{-x}}{2}$$

$$c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot \cos(\theta)$$

$$\sin^2(x) + \cos^2(x) = 1$$

$$a^2 + b^2 = c^2$$

$$e^{i\pi} = -1$$

$$\small{\sin(x) = \frac{e^{ix} - e^{-ix}}{2i}, \cos(x) = \frac{e^{ix} + e^{-ix}}{2}}$$