Trigonomeria

Identidades Trigonom´tricas Fundamentales
e
1.

csc(x) =

1
sin(x)

2.

sec(x) =

1
cos(x)

3.

tan(x) =

sin(x)
cos(x)4.

cot(x) =

cos(x)
tan(x)

5.

1 + tan2 (x) = sec2 (x)

6.

1 + cot2 (x) = csc2 (x)

7.

sin(−x) = − sin(x)

8.cos(−x) = cos(x)

9.

tan(−x) = − tan(x)

10.

11.

cos

π
− x = sin(x)
2

12.

π
− x = cos(x)
2
π
tan
− x = cot(x)
2
sin´
F´rmulas de Suma y Resta de Angulos
o
1.

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

2.

sin(x − y) = sin(x) cos(y) − cos(x) sin(y)3.

cos(x + y) = cos(x) cos(y) − sin(x) sin(y)

4.

cos(x − y) = cos(x) cos(y) + sin(x) sin(y)

5.

tan(x + y) =

6.

tan(x −y) =

tan(x) + tan(y)
1 − tan(x) tan(y)

tan(x) − tan(y)
1 + tan(x) tan(y)

Identidades de Productos
1
(1 − cos (2 x))
2

2.cos2 (x) =

sin (x) cos (x) =

1
sin (2 x)
2

4.

sin (x) sin (y) =

1
(cos (x − y) − cos (x + y))
2

sin (x) cos (y) =

1(sin (x − y) + sin (x + y))
2

6.

cos (x) cos (y) =

1
(cos (x − y) + cos (x + y))
2

1.

sin2 (x) =

3.
5.

1
(1 + cos (2 x))2

´
F´rmulas del Doble de un Angulo
o
1.

sin (2 x) = 2 sin (x) cos (x)

2.

3.

cos (2 x) = 2 cos2 (x) − 1

4.

cos (2 x)= cos2 (x) − sin2 (x)
tan (2 x) =

2 tan (x)
1 − tan2 (x)

(c) Departamento de Matem´ticas. ITESM, Campus Monterrey
a

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