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Basic Trigonometry and Pythagoras' Theorem
Definition of Trigonometric Functions
| Sine | sin x | = | a / c | ||
| Cosine | cos x | = | b / c | ||
| Tangent | tan x | = | a / b | ||
| Cosecant | cosec x | = | c / a | = | 1 / sin x |
| Secant | sec x | = | c / b | = | 1 / cos x |
| Cotangent | cot x | = | b / a | = | 1 / tan x |
Useful Formulae
| sin -x | = | - sin x |
| cos -x | = | cos x |
| sin( x + y ) | = | sin x cos y + cos x sin y |
| sin( x - y ) | = | sin x cos y - cos x sin y |
| cos( x + y ) | = | cos x cos y - sin x sin y |
| cos( x - y ) | = | cos x cos y + sin x sin y |
| sin 2x | = | 2 sin x cos x |
| cos 2x | = | cos2 x - sin2 x |
| = | 2 cos2 x - 1 | |
| = | 1 - 2 sin2 x | |
| tan 2x | = | ( 2 tan x ) / ( 1 - tan2 x ) |
Pythagoras' Theorem
| c2 | = | a2 + b2 |
| 1 | = | sin2 x + cos2 x |
| sec2 x | = | 1 + tan2 x |
| cosec2 x | = | 1 + cot2 x |