# Trigonometry Summary Calculator

## Right Angle Formulas

 sin θ  = Opposite Hypotenuse

 csc θ  = Hypotenuse Opposite

0010
30°π/61/23/23/3
45°π/42/22/21
60°π/33/21/23
90°π/210N/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

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