Trigonmetric Identities
$$\sin {\theta} = \frac {p}{h} = \frac {perpendicular}{hypotenuse} $$
$$\cos {\theta} = \frac {b}{h} = \frac {base}{hypotenuse} $$
$$\tan {\theta} = \frac {p}{b} = \frac {perpendicular}{base} $$
$$\cot {\theta} = \frac {b}{p} = \frac {base}{perpendicular} $$
$$\sec {\theta} = \frac {h}{b} = \frac {hypotenuse}{base} $$
$$\csc {\theta} = \frac {h}{p} = \frac {hypotenuse}{perpendicular} $$
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 | ∞ |
$$\tan {A} = \frac{\sin{A}}{\cos{A}} $$
$$\sec {A} = \frac{1}{\cos{A}}$$
$$cosec A = \frac{1}{\sin{A}}$$
$$\cot {A} = \frac{1}{\tan{A}} = = \frac{\cos {A}}{\sin{A}}$$
$$\sin^2{A} + \cos^2{A} = 1 $$
$$\sec^2{A} = 1 + \tan^2{A}$$
$$\csc^2{A} = 1 + \cot^2{A}$$
$$\sin{A\pm B} = \sin{A}\cos{B}\pm \cos{A}\sin{B}$$
$$\cos{A\pm B} = \cos{A}\cos{B}\mp \sin{A}\sin{B}$$
$$\tan{A\pm B} = \frac{\tan{A}\pm \tan{B}}{\tan{A}\mp \tan{B}}$$
$$\sin{2A} = 2\sin{A}\cos{A} $$
$$\cos{2A} = \cos^2{A} - \sin^2{A} = 2\cos^2{A} - 1 = 1 - 2\sin^2{A} $$
$$\tan{2A} = \frac{2\tan{A}}{1 - \tan^2{A}} $$