From Euclid to Spigotry
Summary of Trigonometry
Last modified: September 9, 2004

sin a = cos b = a/c
cos a = sin b = b/c
tan a = cot b = a/b
cot a = tan b = b/a
sec a = csc b = c/b
csc a = sec b = c/a
Pythagorean Theorem:
a2 + b2 = c2
sin2 a + cos2 a = 1
tan2 a + 1 = sec2 a
1 + cot2 a = csc2 a
Addition formulas:
cos(x+y) = cos x cos y - sin x  sin y
cos(x-y) = cos x cos y + sin x  sin y
sin (x+y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y
tan (x+y) = (tan x + tan y)/(1 - tan x tan y)
sin p/2 = 1      cos p/2 = 0
sin p = 0         cos p = -1
sin 2p = 0       cos 2p = 1
sin p/4 = cos p/4 = 1/
sin p/6 = cos p/3 = 1/2
sin p/3 = cos p/6 = 
Double angle formulas:
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)
cot 2x = (1 - tan2 x)/2 tan x = (cot x - tan x)/2
Half angle fomulas:
sin (x/2) =           tan x/2 =  =  
cos (x/2) =         cot x/2 =  =  

De Moivre's theorem:
 einx = (cos x + i sin x)n = cos nx + i sin nx
Triple angle formulas:
 =  =  
 = 
Law of sines:

Law of cosines: c2 = a2 + b2 - 2 ab cos C