Trigonometric Identities

Home | Teacher | Parents | Glossary | About Us

Email this page to a friend

	Resources
	· Cool Tools · Formulas & Tables · References · Test Preparation · Study Tips · Wonders of Math
	Search

Trigonometric Identities

(Math | Trig | 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

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

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

tan^{^2}(x) + 1 = sec^{^2}(x)

cot^{^2}(x) + 1 = csc^{^2}(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) = cos^{^2}(x) - sin^{^2}(x) = 2 cos^{^2}(x) - 1 = 1 - 2 sin^{^2}(x)

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

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

cos^{^2}(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

sin^{^2}(a) 0/4 1/4 2/4 3/4 4/4

cos^{^2}(a) 4/4 3/4 2/4 1/4 0/4

tan^{^2}(a) 0/4 1/3 2/2 3/1 4/0

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

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

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

(Law of Cosines)

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