Library/Graphics/Trigonometry Reference

Basic Identities
$$\sin \theta = \frac{o}{h}$$

$$\cos \theta = \frac{a}{h}$$

$$\tan \theta = \frac{o}{a}$$





Law of Cosines
$$c^2 = a^2 + b^2 - 2ab \cos C$$

$$b^2 = a^2 + c^2 - 2ac \cos B$$

$$a^2 = b^2 + c^2 - 2bc \cos A$$

Law of Sines
$$ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} $$

Areas of Triangles
$$\textbf{A} = \frac{1}{2} bc \sin A$$

$$\textbf{A} = \frac{1}{2} ac \sin B$$

$$\textbf{A} = \frac{1}{2} ab \sin C$$

$$\textbf{A} = \frac{1}{2} a^2 \frac{\sin B \sin C}{\sin A}$$

$$\textbf{A} = \frac{1}{2} b^2 \frac{\sin A \sin C}{\sin B}$$

$$\textbf{A} = \frac{1}{2} c^2 \frac{\sin A \sin B}{\sin C}$$

$$s = \frac{a+b+c}{2}$$

$$\textbf{A} = \sqrt{ s (s -a) (s - b) (s -c) }$$

Reciprocal Identities
$$sin \alpha = \frac{1}{ \csc \alpha }$$

$$cos \alpha = \frac{1}{ \sec \alpha }$$

$$tan \alpha = \frac {\sin \alpha}{\cos \alpha} = \frac{1}{ \cot \alpha }$$

$$csc \alpha = \frac{1}{ \sin \alpha }$$

$$sec \alpha = \frac{1}{ \cos \alpha }$$

$$cot \alpha = \frac {\cos \alpha}{\sin \alpha} = \frac{1}{ \tan \alpha }$$

$$\sin \alpha \csc \alpha = 1$$

$$\cos \alpha \sec \alpha = 1$$

$$\tan \alpha \cot \alpha = 1$$

Cofunction Identities
$$\sin \alpha = \cos (90^{o} - \alpha)$$

$$\csc \alpha = \sec (90^{o} - \alpha)$$

$$\tan \alpha = \cot (90^{o} - \alpha)$$

$$\cos \alpha = \sin (90^{o} - \alpha)$$

$$\sec \alpha = \csc(90^{o} - \alpha)$$

$$\cot \alpha = \tan (90^{o} - \alpha)$$