Trigonometry Summary Calculator

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Right Angle Formulas

sin θ  =	Opposite
	Hypotenuse

cos θ  =	Adjacent
	Hypotenuse

tan θ  =	Opposite
	Adjacent

csc θ  =	Hypotenuse
	Opposite

sec θ  =	Hypotenuse
	Adjacent

cot θ  =	Adjacent
	Opposite

Important Angle Summary

θ	radians	sinθ	cosθ	tanθ
0°	0	0	1	0
30°	π/6	1/2	√3/2	√3/3
45°	π/4	√2/2	√2/2	1
60°	π/3	√3/2	1/2	√3
90°	π/2	1	0	N/A

Fundamental Identities

tan θ  =	sin θ
	cos θ

csc θ  =	1
	sin θ

sec θ  =	1
	cos θ

cot θ  =	cos θ
	sin θ

cot θ  =	1
	tan θ

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ
sin( - θ) = -sin θ
cos( - θ) = cos θ
tan( - θ) = -tan θ

Addition and Subtraction Formulas

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

tan(x + y)  =	tan x + tan y
	1 - tan x tan y

tan(x - y)  =	tan x - tan y
	1 + tan x tan y

Double-Angle Formulas

sin 2x = 2 sin x cos x
cos 2x = cos²x - sin²x
cos 2x = 2 cos²x - 1
cos 2x = 1 - 2 sin²x

tan 2x  =	2 tan x
	1 - tan2x

Half-Angle Formulas

sin2x  =	1 - cos 2x
	2

cos2x  =	1 + cos 2x
	2

Law of Sines

Given a Triangle with Angles A,B,C and corresponding sides a,b,c

sin A
a

=

sin B
b

=

sin C

c

Law of Cosines

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