Trignometric Ratios for Right Triangle

$$\sin {\theta} = \frac {p}{h} = \frac {perpendicular}{hypotenuse} $$

$$\cos {\theta} = \frac {b}{h} = \frac {base}{hypotenuse} $$

$$\tan {\theta} = \frac {p}{b} = \frac {perpendicular}{base} $$

$$\cot {\theta} = \frac {b}{p} = \frac {base}{perpendicular} $$

$$\sec {\theta} = \frac {h}{b} = \frac {hypotenuse}{base} $$

$$\csc {\theta} = \frac {h}{p} = \frac {hypotenuse}{perpendicular} $$

---

Trignometric Table

θ	0°	30°	45°	60°	90°	120°	180°	270°	360°
sin θ	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1	$\frac{\sqrt{3}}{2}$	0	-1	0
cos θ	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0	$\frac{-1}{2}$	-1	0	1
tan θ	0	$\frac{1}{\sqrt{3}}$	1	$\sqrt{3}$	∞	$-\sqrt{3}$	0	∞	0
cot θ	∞	$\sqrt{3}$	1	$\frac{1}{\sqrt{3}}$	0	$\frac{-1}{\sqrt{3}}$	∞	0	∞
sec θ	1	$\frac{2}{\sqrt{3}}$	$\sqrt{2}$	2	∞	-2	-1	∞	1
cosec θ	∞	2	$\sqrt{2}$	$\frac{2}{\sqrt{3}}$	1	$\frac{1}{\sqrt{3}}$	∞	-1	∞

---

Identities

$$\tan {A} = \frac{\sin{A}}{\cos{A}} $$

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

$$cosec A = \frac{1}{\sin{A}}$$

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

$$\sin^2{A} + \cos^2{A} = 1 $$

$$\sec^2{A} = 1 + \tan^2{A}$$

$$\csc^2{A} = 1 + \cot^2{A}$$

$$\sin{A\pm B} = \sin{A}\cos{B}\pm \cos{A}\sin{B}$$

$$\cos{A\pm B} = \cos{A}\cos{B}\mp \sin{A}\sin{B}$$

$$\tan{A\pm B} = \frac{\tan{A}\pm \tan{B}}{\tan{A}\mp \tan{B}}$$

$$\sin{2A} = 2\sin{A}\cos{A} $$

$$\cos{2A} = \cos^2{A} - \sin^2{A} = 2\cos^2{A} - 1 = 1 - 2\sin^2{A} $$

$$\tan{2A} = \frac{2\tan{A}}{1 - \tan^2{A}} $$

---