English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/2 (arcsin(1)+1/2 sin(2arcsin(1)))

Solución

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

\frac{arcsin ( 1 )}{2}

Notación decimal

0.78539 \dots

Pasos de solución

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1))) = \frac{2 arcsin ( 1 ) + sin ( 2 arcsin ( 1 ) )}{4}

\frac{1}{2} (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

Multiplicar fracciones:

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

= \frac{1 \cdot ( arcsin ( 1 ) + \frac{1}{2} sin ( 2 arcsin ( 1 ) ) )}{2}

1 \cdot (arcsin (1) + \frac{1}{2} sin (2 arcsin (1))) = arcsin (1) + \frac{1}{2} sin (2 arcsin (1))

1 \cdot (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

Multiplicar:

1 \cdot (arcsin (1) + \frac{1}{2} sin (2 arcsin (1))) = (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

= (arcsin (1) + \frac{1}{2} sin (2 arcsin (1)))

Quitar los parentesis:

(a) = a

= arcsin (1) + \frac{1}{2} sin (2 arcsin (1))

= \frac{arcsin ( 1 ) + \frac{1}{2} sin ( 2 arcsin ( 1 ) )}{2}

\frac{1}{2} sin (2 arcsin (1)) = \frac{sin ( 2 arcsin ( 1 ) )}{2}

\frac{1}{2} sin (2 arcsin (1))

Multiplicar fracciones:

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

= \frac{1 \cdot sin ( 2 arcsin ( 1 ) )}{2}

Multiplicar:

1 \cdot sin (2 arcsin (1)) = sin (2 arcsin (1))

= \frac{sin ( 2 arcsin ( 1 ) )}{2}

= \frac{arcsin ( 1 ) + \frac{s i n ( 2 a r c s i n ( 1 ) )}{2}}{2}

Simplificar

arcsin (1) + \frac{sin ( 2 arcsin ( 1 ) )}{2}

en una fracción:

\frac{2 arcsin ( 1 ) + sin ( 2 arcsin ( 1 ) )}{2}

arcsin (1) + \frac{sin ( 2 arcsin ( 1 ) )}{2}

Convertir a fracción:

arcsin (1) = \frac{arcsin ( 1 ) 2}{2}

= \frac{arcsin ( 1 ) \cdot 2}{2} + \frac{sin ( 2 arcsin ( 1 ) )}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{arcsin ( 1 ) \cdot 2 + sin ( 2 arcsin ( 1 ) )}{2}

= \frac{\frac{2 a r c s i n ( 1 ) + s i n ( 2 a r c s i n ( 1 ) )}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{arcsin ( 1 ) \cdot 2 + sin ( 2 arcsin ( 1 ) )}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{2 arcsin ( 1 ) + sin ( 2 arcsin ( 1 ) )}{4}

= \frac{2 arcsin ( 1 ) + sin ( 2 arcsin ( 1 ) )}{4}

Re-escribir usando identidades trigonométricas:

sin (2 arcsin (1)) = 2 sin (arcsin (1)) cos (arcsin (1))

sin (2 arcsin (1))

Utilizar la identidad trigonométrica del ángulo doble:

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

= 2 sin (arcsin (1)) cos (arcsin (1))

= \frac{2 arcsin ( 1 ) + 2 sin ( arcsin ( 1 ) ) cos ( arcsin ( 1 ) )}{4}

Re-escribir usando identidades trigonométricas:

sin (arcsin (1)) = 1

Usar la siguiente identidad:

sin (arcsin (x)) = x

= 1

Re-escribir usando identidades trigonométricas:

cos (arcsin (1)) = 0

cos (arcsin (1))

Re-escribir usando identidades trigonométricas:

cos (arcsin (1)) = 1 - 1^{2}

Usar la siguiente identidad:

cos (arcsin (x)) = 1 - x^{2}

= 1 - 1^{2}

= 1 - 1^{2}

Simplificar

= 0

= \frac{2 arcsin ( 1 ) + 2 \cdot 1 \cdot 0}{4}

Simplificar

\frac{2 arcsin ( 1 ) + 2 \cdot 1 \cdot 0}{4} : \frac{arcsin ( 1 )}{2}

\frac{2 arcsin ( 1 ) + 2 \cdot 1 \cdot 0}{4}

2 arcsin (1) + 2 \cdot 1 \cdot 0 = 2 arcsin (1)

2 arcsin (1) + 2 \cdot 1 \cdot 0

Aplicar la regla

0 \cdot a = 0

= 2 arcsin (1) + 0

2 arcsin (1) + 0 = 2 arcsin (1)

= 2 arcsin (1)

= \frac{2 arcsin ( 1 )}{4}

Eliminar los terminos comunes:

2

= \frac{arcsin ( 1 )}{2}

= \frac{arcsin ( 1 )}{2}

(3 sin (1 0^{\circ}) + cos (1 0^{\circ})) csc (4 0^{\circ})

\frac{tan ( 0 ) \cdot cos ( 0 )}{sin ( 0 )}

15 sin (8 5^{\circ})

sec (22 0^{\circ})

sin (π \frac{1}{4})