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Popular Trigonometría >

250sin(75)=393.19sin(45-θ)

Solución

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

Solución

θ = - 36 0^{\circ} n + 4 5^{\circ} - 0.66132 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + 0.66132 \dots

Radianes

θ = \frac{π}{4} - 0.66132 \dots - 2 πn, θ = - π + \frac{π}{4} + 0.66132 \dots - 2 πn

Pasos de solución

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

sin (7 5^{\circ}) = \frac{6 + 2}{4}

sin (7 5^{\circ})

Re-escribir usando identidades trigonométricas:

sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

sin (7 5^{\circ})

Escribir

sin (7 5^{\circ})

como

sin (4 5^{\circ} + 3 0^{\circ})

= sin (4 5^{\circ} + 3 0^{\circ})

Utilizar la identidad de suma de ángulos:

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

= sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

= sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 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:

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:

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

cos (4 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 (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} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

Simplificar

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

\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}

250 \cdot \frac{6 + 2}{4} = 393.19 sin (4 5^{\circ} - θ)

Intercambiar lados

393.19 sin (4 5^{\circ} - θ) = 250 \cdot \frac{6 + 2}{4}

Multiplicar ambos lados por

100

393.19 sin (4 5^{\circ} - θ) = 250 \cdot \frac{6 + 2}{4}

Para eliminar los puntos decimales, multiplique por 10 por cada digito después del punto decimalHay digitos

2

a la derecha del punto decimal, por lo que debe multiplicar por

100

393.19 sin (4 5^{\circ} - θ) \cdot 100 = 250 \cdot \frac{6 + 2}{4} \cdot 100

Simplificar

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

Dividir ambos lados entre

39319

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

Dividir ambos lados entre

39319

\frac{39319 sin ( 4 5 ^{\circ} - θ )}{39319} = \frac{6250 ( 6 + 2 )}{39319}

Simplificar

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

Aplicar propiedades trigonométricas inversas

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

Soluciones generales para

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n, 4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n, 4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

Resolver

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n : θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

Desplace

4 5^{\circ}

a la derecha

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

Restar

4 5^{\circ}

de ambos lados

4 5^{\circ} - θ - 4 5^{\circ} = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

Simplificar

- θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

- θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

Dividir ambos lados entre

- 1

- θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

Dividir ambos lados entre

- 1

\frac{- θ}{- 1} = \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

Simplificar

\frac{- θ}{- 1} = \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

Simplificar

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{θ}{1}

Aplicar la regla

\frac{a}{1} = a

= θ

Simplificar

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} : - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

Agrupar términos semejantes

= \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} + \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{4 5 ^{\circ}}{- 1} + \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{4 5 ^{\circ}}{- 1} = - 4 5^{\circ}

\frac{4 5 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4 5 ^{\circ}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{4 5 ^{\circ}}{1} = 4 5^{\circ}

= - 4 5^{\circ}

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} = - arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1} = arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - 36 0^{\circ} n - (- 4 5^{\circ}) - arcsin (\frac{6250 ( 6 + 2 )}{39319})

Aplicar la regla

- (- a) = a

= - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

Resolver

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n : θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

Desplace

4 5^{\circ}

a la derecha

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

Restar

4 5^{\circ}

de ambos lados

4 5^{\circ} - θ - 4 5^{\circ} = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

Simplificar

- θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

- θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

Dividir ambos lados entre

- 1

- θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n - 4 5^{\circ}

Dividir ambos lados entre

- 1

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

Simplificar

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

Simplificar

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{θ}{1}

Aplicar la regla

\frac{a}{1} = a

= θ

Simplificar

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1}

Agrupar términos semejantes

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - 18 0^{\circ}

Aplicar la regla

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{4 5 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{4 5 ^{\circ}}{- 1} - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

\frac{4 5 ^{\circ}}{- 1} = - 4 5^{\circ}

\frac{4 5 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4 5 ^{\circ}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{4 5 ^{\circ}}{1} = 4 5^{\circ}

= - 4 5^{\circ}

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1} = - arcsin (\frac{6250 ( 6 + 2 )}{39319})

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{arcsin ( \frac{6250 ( 6 + 2 )}{39319} )}{1} = arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - arcsin (\frac{6250 ( 6 + 2 )}{39319})

= - 18 0^{\circ} - 36 0^{\circ} n - (- 4 5^{\circ}) - (- arcsin (\frac{6250 ( 6 + 2 )}{39319}))

Aplicar la regla

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}), θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

Mostrar soluciones en forma decimal

θ = - 36 0^{\circ} n + 4 5^{\circ} - 0.66132 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + 0.66132 \dots

Gráfica

Ejemplos populares

tan(θ)= 6/(6.71)

sin(2θ)=0.5

cos(pi/2+x)=0

4sin(x)-13=2cos^2(x)-9

cos(θ)=-8/11