Math2.org Math Tables: Trigonometric Identities

sin(theta) = a / c	csc(theta) = 1 / sin(theta) = c / a
cos(theta) = b / c	sec(theta) = 1 / cos(theta) = c / b
tan(theta) = sin(theta) / cos(theta) = a / b	cot(theta) = 1/ tan(theta) = b / a

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sin(-x) = -sin(x)
csc(-x) = -csc(x)
cos(-x) = cos(x)
sec(-x) = sec(x)
tan(-x) = -tan(x)
cot(-x) = -cot(x)

sin2(x) + cos2(x) = 1	tan2(x) + 1 = sec2(x)	cot2(x) + 1 = csc2(x)
sin(x y) = sin x cos y cos x sin y
cos(x y) = cos x cosy sin x sin y

tan(x y) = (tan x tan y) / (1 tan x tan 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))

sin²(x) = 1/2 - 1/2 cos(2x)

cos²(x) = 1/2 + 1/2 cos(2x)

sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )

cos x - cos y = -2 sin( (x-y)/2 ) sin( (x + y)/2 )

Trig Table of Common Angles

angle	0	30	45	60	90
sin2(a)	0/4	1/4	2/4	3/4	4/4
cos2(a)	4/4	3/4	2/4	1/4	0/4
tan2(a)	0/4	1/3	2/2	3/1	4/0

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Given Triangle abc, with angles A,B,C; a is opposite to A, b oppositite B, c opposite C:

a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines)

c2 = a2 + b2 - 2ab cos(C) b2 = a2 + c2 - 2ac cos(B) a2 = b2 + c2 - 2bc cos(A)

(Law of Cosines)

(a - b)/(a + b) = tan 1/2(A-B) / tan 1/2(A+B) (Law of Tangents)