Sinx 2 Cosx 2 1

Trigonometric Identities

(Math | Trig | Identities)

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

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sin(-x) = -sin(10)
csc(-x) = -csc(x)
cos(-10) = cos(x)
sec(-x) = sec(x)
tan(-10) = -tan(x)
cot(-x) = -cot(x)

sin^two(x) + cos^two(x) = 1	tan^two(x) + 1 = sec^ii(x)	cot^2(x) + 1 = csc^two(x)
sin(x y) = sin x cos y cos ten sin y
cos(x y) = cos x cosy sin x sin y

tan(10 y) = (tan 10 tan y) / (1 tan x tan y)

sin(2x) = ii sin x cos x

cos(2x) = cos^{^2}(x) - sin^{^2}(x) = ii cos^{^two}(x) - 1 = 1 - 2 sin^{^2}(x)

tan(2x) = 2 tan(x) / (1 - tan^{^ii}(x))

sin^{^ii}(ten) = ane/two - 1/2 cos(2x)

cos^{^2}(x) = 1/2 + 1/2 cos(2x)

sin x - sin y = 2 sin( (10 - y)/2 ) cos( (x + y)/2 )

cos 10 - cos y = -ii sin( (x - y)/2 ) sin( (x + y)/ii )

Trig Table of Mutual Angles

angle	0	30	45	60	ninety
sin^2(a)	0/4	1/4	2/4	3/four	4/4
cos^2(a)	4/4	three/4	2/4	1/4	0/4
tan^2(a)	0/4	ane/3	2/2	iii/1	4/0

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

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

c^2 = a^ii + b^2 - 2ab cos(C) b^2 = a^2 + c^2 - 2ac cos(B) a^2 = b^2 + c^ii - 2bc cos(A)

(Police of Cosines)

(a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2] (Constabulary of Tangents)

Sinx 2 Cosx 2 1,

Source: http://www.math.com/tables/trig/identities.htm

Posted by: underwoodcolowerve.blogspot.com

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