Trignometric Ratios for Right Triangle

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

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

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

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

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

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

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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	∞

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Identities

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

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

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

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

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

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

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

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

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

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

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

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

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

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