Formula sheet

USEFUL TRIGONOMETRIC IDENTITIES

Definitions
sin x
tan x =
cos x
1 1 1
sec x = cosec x = cot x =
cos x sin x tan x


Fundamental trig identity
(cos x)2 + (sin x)2 = 1
1 + (tan x)2 = (sec x)2
(cot x)2 + 1 = (cosec x)2



Odd and even properties
cos(−x) = cos(x) sin(−x) = − sin(x) tan(−x) = − tan(x)



Double angle formulas
sin(2x) = 2 sin x cos x cos(2x) = (cos x)2 − (sin x)2
cos(2x) = 2(cos x)2 − 1
cos(2x) = 1 − 2(sin x)2



Half angle formulas
2
sin( 21 x) = 21 (1 − cos x)

2
cos( 21 x) = 21 (1 + cos x)




Sums and differences of angles
cos(A + B) = cos A cos B − sin A sin B
cos(A − B) = cos A cos B + sin A sin B
sin(A + B) = sin A cos B + cos A sin B
sin(A − B) = sin A cos B − cos A sin B


** See other side for more identities **