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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