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Popular >

cos(285)-cos(165)

Solución

cos (28 5^{\circ}) - cos (16 5^{\circ})

Solución

\frac{6}{2}

Notación decimal

1.22474 \dots

Pasos de solución

cos (28 5^{\circ}) - cos (16 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos (28 5^{\circ}) = \frac{2 ( 3 - 1 )}{4}

cos (28 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos (15 0^{\circ}) cos (13 5^{\circ}) - sin (15 0^{\circ}) sin (13 5^{\circ})

cos (28 5^{\circ})

Escribir

cos (28 5^{\circ})

como

cos (15 0^{\circ} + 13 5^{\circ})

= cos (15 0^{\circ} + 13 5^{\circ})

Utilizar la identidad de suma de ángulos:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (15 0^{\circ}) cos (13 5^{\circ}) - sin (15 0^{\circ}) sin (13 5^{\circ})

= cos (15 0^{\circ}) cos (13 5^{\circ}) - sin (15 0^{\circ}) sin (13 5^{\circ})

Utilizar la siguiente identidad trivial:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 0^{\circ})

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{3}{2}

Utilizar la siguiente identidad trivial:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\circ})

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

Utilizar la siguiente identidad trivial:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

Utilizar la siguiente identidad trivial:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= (- \frac{3}{2}) (- \frac{2}{2}) - \frac{1}{2} \cdot \frac{2}{2}

Simplificar

(- \frac{3}{2}) (- \frac{2}{2}) - \frac{1}{2} \cdot \frac{2}{2} : \frac{2 ( 3 - 1 )}{4}

(- \frac{3}{2}) (- \frac{2}{2}) - \frac{1}{2} \cdot \frac{2}{2}

Quitar los parentesis:

(- a) = - a, - (- a) = a

= \frac{3}{2} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{2}{2}

Factorizar el termino común

\frac{2}{2}

= \frac{2}{2} (\frac{3}{2} - \frac{1}{2})

\frac{3}{2} - \frac{1}{2} = \frac{3 - 1}{2}

\frac{3}{2} - \frac{1}{2}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 - 1}{2}

= \frac{2}{2} \cdot \frac{3 - 1}{2}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( 3 - 1 ) 2}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{2 ( 3 - 1 )}{4}

= \frac{2 ( 3 - 1 )}{4}

Re-escribir usando identidades trigonométricas:

cos (16 5^{\circ}) = \frac{- 6 - 2}{4}

cos (16 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

cos (16 5^{\circ})

Escribir

cos (16 5^{\circ})

como

cos (13 5^{\circ} + 3 0^{\circ})

= cos (13 5^{\circ} + 3 0^{\circ})

Utilizar la identidad de suma de ángulos:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

= cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

Utilizar la siguiente identidad trivial:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\circ})

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

Utilizar la siguiente identidad trivial:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

Utilizar la siguiente identidad trivial:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

Utilizar la siguiente identidad trivial:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= (- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplificar

(- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{- 6 - 2}{4}

(- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Quitar los parentesis:

(- a) = - a

= - \frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

\frac{2}{2} \cdot \frac{3}{2}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 3}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{2 3}{4}

Simplificar

23 : 6

23

Aplicar las leyes de los exponentes:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiplicar los numeros:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

\frac{2}{2} \cdot \frac{1}{2}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 1}{2 \cdot 2}

Multiplicar:

2 \cdot 1 = 2

= \frac{2}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{2}{4}

= - \frac{6}{4} - \frac{2}{4}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 6 - 2}{4}

= \frac{- 6 - 2}{4}

= \frac{2 ( 3 - 1 )}{4} - \frac{- 6 - 2}{4}

Simplificar

\frac{2 ( 3 - 1 )}{4} - \frac{- 6 - 2}{4} : \frac{6}{2}

\frac{2 ( 3 - 1 )}{4} - \frac{- 6 - 2}{4}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 ( 3 - 1 ) - ( - 6 - 2 )}{4}

Expandir

2 (3 - 1) - (- 6 - 2) : 26

2 (3 - 1) - (- 6 - 2)

Expandir

2 (3 - 1) : 6 - 2

2 (3 - 1)

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 2, b = 3, c = 1

= 23 - 2 \cdot 1

= 23 - 1 \cdot 2

Simplificar

23 - 1 \cdot 2 : 6 - 2

23 - 1 \cdot 2

23 = 6

23

Aplicar las leyes de los exponentes:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiplicar los numeros:

2 \cdot 3 = 6

= 6

1 \cdot 2 = 2

1 \cdot 2

Multiplicar:

1 \cdot 2 = 2

= 2

= 6 - 2

= 6 - 2

= 6 - 2 - (- 6 - 2)

- (- 6 - 2) : 6 + 2

- (- 6 - 2)

Poner los parentesis

= - (- 6) - (- 2)

Aplicar las reglas de los signos

- (- a) = a

= 6 + 2

= 6 - 2 + 6 + 2

Simplificar

6 - 2 + 6 + 2 : 26

6 - 2 + 6 + 2

Sumar elementos similares:

- 2 + 2 = 0

= 6 + 6

Sumar elementos similares:

6 + 6 = 26

= 26

= 26

= \frac{2 6}{4}

Eliminar los terminos comunes:

2

= \frac{6}{2}

= \frac{6}{2}

Ejemplos populares

arcsin(5/2)

arcsin (\frac{5}{2})

arctan((sqrt(3))/4)

arctan (\frac{3}{4})

arctan(7/7)

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8sin(10)

8 sin (1 0^{\circ})

cot((-pi)/3)

cot (\frac{- π}{3})