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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

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