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cos(θ/2)=sqrt((1+3/5)/2)

Solución

cos (\frac{θ}{2}) = \frac{1 + \frac{3}{5}}{2}

Solución

θ = 2 \cdot 0.46364 \dots + 4 πn, θ = 4 π - 2 \cdot 0.46364 \dots + 4 πn

radianes

θ = 0.92729 \dots + 12.56637 \dots n, θ = 11.63907 \dots + 12.56637 \dots n

Pasos de solución

cos (\frac{θ}{2}) = \frac{1 + \frac{3}{5}}{2}

Simplificar

\frac{1 + \frac{3}{5}}{2} : \frac{2 5}{5}

\frac{1 + \frac{3}{5}}{2}

\frac{1 + \frac{3}{5}}{2} = \frac{4}{5}

\frac{1 + \frac{3}{5}}{2}

Simplificar

1 + \frac{3}{5}

en una fracción:

\frac{8}{5}

1 + \frac{3}{5}

Convertir a fracción:

1 = \frac{1 \cdot 5}{5}

= \frac{1 \cdot 5}{5} + \frac{3}{5}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot 5 + 3}{5}

1 \cdot 5 + 3 = 8

1 \cdot 5 + 3

Multiplicar los numeros:

1 \cdot 5 = 5

= 5 + 3

Sumar:

5 + 3 = 8

= 8

= \frac{8}{5}

= \frac{\frac{8}{5}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{8}{5 \cdot 2}

Multiplicar los numeros:

5 \cdot 2 = 10

= \frac{8}{10}

Eliminar los terminos comunes:

2

= \frac{4}{5}

= \frac{4}{5}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{4}{5}

4 = 2

4

Descomponer el número en factores primos:

4 = 2^{2}

= 2^{2}

Aplicar las leyes de los exponentes:

2^{2} = 2

= 2

= \frac{2}{5}

Racionalizar

\frac{2}{5} : \frac{2 5}{5}

\frac{2}{5}

Multiplicar por el conjugado

\frac{5}{5}

= \frac{2 5}{5 5}

55 = 5

55

Aplicar las leyes de los exponentes:

a a = a

55 = 5

= 5

= \frac{2 5}{5}

= \frac{2 5}{5}

cos (\frac{θ}{2}) = \frac{2 5}{5}

Aplicar propiedades trigonométricas inversas

cos (\frac{θ}{2}) = \frac{2 5}{5}

Soluciones generales para

cos (\frac{θ}{2}) = \frac{2 5}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{θ}{2} = arccos (\frac{2 5}{5}) + 2 πn, \frac{θ}{2} = 2 π - arccos (\frac{2 5}{5}) + 2 πn

\frac{θ}{2} = arccos (\frac{2 5}{5}) + 2 πn, \frac{θ}{2} = 2 π - arccos (\frac{2 5}{5}) + 2 πn

Resolver

\frac{θ}{2} = arccos (\frac{2 5}{5}) + 2 πn : θ = 2 arccos (\frac{2}{5}) + 4 πn

\frac{θ}{2} = arccos (\frac{2 5}{5}) + 2 πn

Simplificar

arccos (\frac{2 5}{5}) + 2 πn : arccos (\frac{2}{5}) + 2 πn

arccos (\frac{2 5}{5}) + 2 πn

\frac{2 5}{5} = \frac{2}{5}

\frac{2 5}{5}

Aplicar las leyes de los exponentes:

5 = 5^{\frac{1}{2}}

= \frac{2 \cdot 5 ^{\frac{1}{2}}}{5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{5 ^{\frac{1}{2}}}{5 ^{1}} = \frac{1}{5 ^{1 - \frac{1}{2}}}

= \frac{2}{5 ^{1 - \frac{1}{2}}}

Restar:

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

= \frac{2}{5 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

5^{\frac{1}{2}} = 5

= \frac{2}{5}

= arccos (\frac{2}{5}) + 2 πn

\frac{θ}{2} = arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

2

\frac{θ}{2} = arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

2

\frac{2 θ}{2} = 2 arccos (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

\frac{2 θ}{2} = 2 arccos (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

2 arccos (\frac{2}{5}) + 2 \cdot 2 πn : 2 arccos (\frac{2}{5}) + 4 πn

2 arccos (\frac{2}{5}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 2 arccos (\frac{2}{5}) + 4 πn

θ = 2 arccos (\frac{2}{5}) + 4 πn

θ = 2 arccos (\frac{2}{5}) + 4 πn

θ = 2 arccos (\frac{2}{5}) + 4 πn

Resolver

\frac{θ}{2} = 2 π - arccos (\frac{2 5}{5}) + 2 πn : θ = 4 π - 2 arccos (\frac{2}{5}) + 4 πn

\frac{θ}{2} = 2 π - arccos (\frac{2 5}{5}) + 2 πn

Simplificar

2 π - arccos (\frac{2 5}{5}) + 2 πn : 2 π - arccos (\frac{2}{5}) + 2 πn

2 π - arccos (\frac{2 5}{5}) + 2 πn

\frac{2 5}{5} = \frac{2}{5}

\frac{2 5}{5}

Aplicar las leyes de los exponentes:

5 = 5^{\frac{1}{2}}

= \frac{2 \cdot 5 ^{\frac{1}{2}}}{5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{5 ^{\frac{1}{2}}}{5 ^{1}} = \frac{1}{5 ^{1 - \frac{1}{2}}}

= \frac{2}{5 ^{1 - \frac{1}{2}}}

Restar:

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

= \frac{2}{5 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

5^{\frac{1}{2}} = 5

= \frac{2}{5}

= 2 π - arccos (\frac{2}{5}) + 2 πn

\frac{θ}{2} = 2 π - arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

2

\frac{θ}{2} = 2 π - arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

2

\frac{2 θ}{2} = 2 \cdot 2 π - 2 arccos (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

\frac{2 θ}{2} = 2 \cdot 2 π - 2 arccos (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

2 \cdot 2 π - 2 arccos (\frac{2}{5}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{2}{5}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{2}{5}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{2}{5}) + 4 πn

θ = 4 π - 2 arccos (\frac{2}{5}) + 4 πn

θ = 4 π - 2 arccos (\frac{2}{5}) + 4 πn

θ = 4 π - 2 arccos (\frac{2}{5}) + 4 πn

θ = 2 arccos (\frac{2}{5}) + 4 πn, θ = 4 π - 2 arccos (\frac{2}{5}) + 4 πn

Mostrar soluciones en forma decimal

θ = 2 \cdot 0.46364 \dots + 4 πn, θ = 4 π - 2 \cdot 0.46364 \dots + 4 πn

Ejemplos populares

cos(θ)= 35/37

cos (θ) = \frac{35}{37}

-pi/2 =1-2sin(x)

- \frac{π}{2} = 1 - 2 sin (x)

sin(θ)=-0.2761

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sin(3x)=sin(2x+50)

sin (3 x) = sin (2 x + 50)

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(r - c) = a 2 sin (θ) + d