This document contains formulas and theorems related to trigonometry. It includes fundamental trigonometric equations, formulas for trigonometric ratios of summed and subtracted angles, ratios for doubled and halved angles, transformations of sums to products, and theorems for solving triangles using sine, cosine, and tangent functions.

1. Matemáticas Fórmulas trigonométricas
Ecuaciones fundamentales de la trigonometría
sen 2 x + cos 2 x = 1
1 + tg 2 x = sec 2 x
1 + cot g 2 x = cos ec 2 x
Razones trigonométricas de la suma Razones trigonométricas de la
de dos ángulos diferencia de dos ángulos
sen(a + b) = sena ⋅ cos b + senb ⋅ cos a sen(a − b) = sena ⋅ cos b − senb ⋅ cos a
cos(a + b) = cos a ⋅ cos b − sena ⋅ senb cos(a − b) = cos a ⋅ cos b + sena ⋅ senb
tga + tgb tga − tgb
tg (a + b) = tg (a − b) =
1 − tga ⋅ tgb 1 + tga ⋅ tgb
Razones del ángulo doble Razones del ángulo mitad
sen 2a = 2 sena ⋅ cos a a 1 − cos a
sen =±
cos 2a = cos 2 a − sen 2 a 2 2
tg 2a =
2tga a 1 + cos a
cos =±
1 − tg 2 a 2 2
a 1 − cos a
tg =±
2 1 + cos a
Transformación de sumas en productos
A+ B A− B
senA + senB = 2 sen( ) ⋅ cos( )
2 2
A+ B A− B
senA − senB = 2 cos( ) ⋅ sen( )
2 2
A+ B A− B
cos A + cos B = 2 cos( ) ⋅ cos( )
2 2
A+ B A− B
cos A − cos B = −2sen( ) ⋅ sen( )
2 2
Resolución de triángulos
TEOREMA DEL SENO TEOREMA DEL COSENO
a
=
b
=
c a 2 = b 2 + c 2 − 2bc ⋅ cos A
sena senB senC
b 2 = a 2 + c 2 − 2ac ⋅ cos B
c 2 = a 2 + b 2 − 2ab ⋅ cos C
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