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Identidades de trigonometría
(Mathemática | Trigonometría | Identidades)

sen(theta) = a / c

csc(theta) = 1 / sen(theta) = c / a

cos(theta) = b / c

sec(theta) = 1 / cos(theta) = c / b

tan(theta) = sen(theta) / cos(theta) = a / b

cot(theta) = 1/ tan(theta) = b / a


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

sen^2(x) + cos^2(x) = 1

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

cot^2(x) + 1 = csc^2(x)

sen(x y) = sen x cos y cos x sen y

cos(x y) = cos x cosy sen x sen y

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

sen(2x) = 2 sen x cos x

cos(2x) = cos^2(x) - sen^2(x) = 2 cos^2(x) - 1 = 1 - 2 sen^2(x)

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

sen^2(x) = 1/2 - 1/2 cos(2x)

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

sen x - sen y = 2 sen( (x - y)/2 ) cos( (x + y)/2 )

cos x - cos y = -2 sen( (x-y)/2 ) sen( (x + y)/2 )

Tabla trig de ángulos ordinarios
ángulo 0 30 45 60 90
sen^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


Dado un triángulo abc, con ángulos A,B,C; a está opuesto a A; b opuesto a B; c opuesto a C,

a/sen(A) = b/sen(B) = c/sen(C) (La ley del seno)

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)

(La ley del coseno)

(a - b)/(a + b) = tan 1/2(A-B) / tan 1/2(A+B) (La ley de la tangente)

  
 
  

 
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