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Tablas+Trigonometricas.pdf
1.
Matemática Tabla de propiedades VALORES
DE LAS FUNCIONES TRIGONOMÉTRICAS PARA LOS ÁNGULOS MULTIPLOS DE 30º Y 45º (π π π π/6 Y π π π π/4) Función Ángulos del 1er. cuadrante Ángulos del 2do. cuadrante Ángulos del 3er. cuadrante Ángulos del 4to. cuadrante 0º 30º 45º 60º 90º 120º 135º 150º 180º 210º 225º 240º 270º 300º 315º 330º 360º 0 6 π 4 π 3 π 2 π 3 2π 4 3π 6 5π π 6 7π 4 5π 3 4π 2 3π 3 5π 4 7π 6 11π π 2 sen 0 2 1 2 2 2 3 1 2 3 2 2 2 1 0 2 1 − − − − 2 2 − − − − 2 3 − − − − 1 − − − − 2 3 − − − − 2 2 − − − − 2 1 − − − − 0 cos 1 2 3 2 2 2 1 0 2 1 − − − − 2 2 − − − − 2 3 − − − − 1 − − − − 2 3 − − − − 2 2 − − − − 2 1 − − − − 0 2 1 2 2 2 3 1 tg 0 3 3 1 3 3 − − − − 1 − − − − 3 3 − − − − 0 3 3 1 3 3 − − − − 1 − − − − 3 3 − − − − 0 ctg 3 1 3 3 0 3 3 − − − − 1 − − − − 3 − − − − 3 1 3 3 0 3 3 − − − − 1 − − − − 3 − − − − sec 1 3 3 2 2 2 2 − − − − 2 − − − − 3 3 2 − − − − 1 − − − − 3 3 2 − − − − 2 − − − − 2 − − − − 2 2 3 3 2 1 cosec 2 2 3 3 2 1 3 3 2 2 2 2 − − − − 2 − − − − 3 3 2 − − − − 1 − − − − 3 3 2 − − − − 2 − − − − 2 − − − − FÓRMULAS FUNDAMENTALES DE LA TRIGONOMETRÍA Funciones de un ángulo: 1. 1 cos sen 2 2 = = = = + + + + α α 2. 1 tg sec 2 2 = = = = − − − − α α 3. 1 tg c csc 2 2 = = = = − − − − α α 4. tg cos sen = = = = α α 5. α α α tg c sen cos = = = = 6. 1 csc sen = = = = ⋅ ⋅ ⋅ ⋅ α α 7. 1 sec cos = = = = ⋅ ⋅ ⋅ ⋅ α α 8. 1 tg c tg = = = = ⋅ ⋅ ⋅ ⋅ α α Expresión de una función mediante otra (del mismo ángulo): 1. α α α α α α α α csc 1 sec 1 sec tg c 1 1 tg 1 tg cos 1 sen 2 2 2 2 = = = = − − − − ± ± ± ± = = = = + + + + ± ± ± ± = = = = + + + + ± ± ± ± = = = = − − − − ± ± ± ± = = = = 2. α α α α α α α α csc 1 csc sec 1 tg c 1 tg c tg 1 1 sen 1 cos 2 2 2 2 − − − − ± ± ± ± = = = = = = = = + + + + ± ± ± ± = = = = + + + + ± ± ± ± = = = = − − − − ± ± ± ± = = = = 3. 1 csc 1 1 sec tg c 1 cos cos 1 sen 1 sen tg 2 2 2 2 − − − − ± ± ± ± = = = = − − − − ± ± ± ± = = = = = = = = − − − − ± ± ± ± = = = = − − − − ± ± ± ± = = = = α α α α α α α α 4. 1 csc 1 sec 1 tg 1 cos 1 cos sen sen 1 tg c 2 2 2 2 − − − − ± ± ± ± = = = = − − − − ± ± ± ± = = = = = = = = − − − − ± ± ± ± = = = = − − − − ± ± ± ± = = = = α α α α α α α α Fórmulas de conversión: Para cada circunferencia de ángulo central α, se mide por la razón entre del arco l correspondiente a este ángulo y la longitud del radio r de ésta circunferencia: r l = = = = α ) radianes ( 180 º π α α = = = = ; 180 º ) radianes ( πα α = = = = 8 8 8 8 8 8 8 8 8 8
2.
Matemática Tabla de propiedades Funciones
de la suma y la diferencia de ángulos: 1. β α β α β α sen cos cos sen ) sen( ± ± ± ± = = = = ± ± ± ± 2. β α β α β α sen sen cos cos ) cos( m ± ± ± ± 3. β α β α β α tg tg 1 tg tg ) tg( m ± ± ± ± = = = = ± ± ± ± 4. α β β α β α tg c tg c 1 tg c tg c ) tg( c ± ± ± ± = = = = ± ± ± ± m 5. γ β α γ β α γ β α γ β α γ β α sen sen sen sen cos cos cos sen cos cos cos sen ) sen( − − − − + + + + + + + + + + + + = = = = + + + + + + + + 6. γ β α γ β α γ β α γ β α γ β α sen sen cos sen cos sen cos sen sen cos cos cos ) cos( − − − − − − − − − − − − − − − − = = = = + + + + + + + + Funciones de ángulos múltiples: 1. α α α cos sen 2 2 sen = = = = 2. α α α 3 sen 4 sen 3 3 sen − − − − = = = = 3. α α α α α sen cos 4 sen cos 8 4 sen 3 − − − − = = = = 4. α α α 2 2 sen cos 2 cos − − − − = = = = 5. α α α cos 3 cos 4 3 cos 3 − − − − = = = = 6. 1 cos 8 cos 8 4 cos 2 4 + + + + − − − − = = = = α α 7. α α α 2 tg 1 tg 2 2 tg − − − − = = = = 8. α α α α 2 3 tg 3 1 tg tg 3 3 tg − − − − − − − − = = = = 9. α α α α α 2 2 3 tg tg 6 1 tg 4 tg 4 4 tg + + + + − − − − − − − − = = = = 10. α α α tg c 2 1 tg c 2 tg c 2 − − − − = = = = 11. 1 tg c 3 tg c 3 tg c 3 tg c 2 3 − − − − − − − − = = = = α α α α 12. α α α α α tg c 4 tg c 4 1 tg c 6 tg c tg c 3 2 4 − − − − + + + + − − − − = = = = Funciones de ángulo mitad: 1. 2 cos 1 2 sen α α − − − − ± ± ± ± = = = = 2. 2 cos 1 2 cos α α + + + + ± ± ± ± = = = = 3. α α α α α α α cos 1 sen sen cos 1 cos 1 cos 1 2 tg + + + + = = = = − − − − = = = = + + + + − − − − ± ± ± ± = = = = 4. α α α α α α α cos 1 sen sen cos 1 cos 1 cos 1 2 tg c − − − − = = = = + + + + = = = = − − − − + + + + ± ± ± ± = = = = Suma y diferencia de funciones: 1. − − − − + + + + = = = = + + + + 2 cos 2 sen 2 sen sen β α β α β α 2. − − − − + + + + = = = = − − − − 2 sen 2 cos 2 sen sen β α β α β α 3. − − − − + + + + = = = = + + + + 2 cos 2 cos 2 cos cos β α β α β α 4. − − − − + + + + = = = = − − − − 2 sen 2 sen 2 cos cos β α β α β α 5. β α β α β α cos cos ) sen( tg tg ± ± ± ± = = = = ± ± ± ± 6. β α β α β α sen sen ) sen( tg c tg c ± ± ± ± ± ± ± ± = = = = ± ± ± ± 7. β α β α β α sen cos ) cos( tg c tg − − − − = = = = + + + + 8. β α β α β α cos sen ) cos( tg tg c + + + + = = = = − − − − Producto de funciones: 1. ( ( ( ( ) ) ) ) ) cos( ) cos( 2 1 sen sen β α β α β α + + + + − − − − − − − − = = = = 2. ( ( ( ( ) ) ) ) ) cos( ) cos( 2 1 cos cos β α β α β α + + + + + + + + − − − − = = = = 3. ( ( ( ( ) ) ) ) ) sen( ) sen( 2 1 cos sen β α β α β α + + + + + + + + − − − − = = = =
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