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Popular >

(sin(θ))/(140)=(sin(110))/(622)

Solución

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

Solución

θ = 0.21311 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21311 \dots + 36 0^{\circ} n

+1

radianes

θ = 0.21311 \dots + 2 πn, θ = π - 0.21311 \dots + 2 πn

Pasos de solución

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

Multiplicar ambos lados por

10

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

Multiplicar ambos lados por

10

\frac{sin ( θ )}{140} \cdot 10 = \frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

Simplificar

\frac{sin ( θ )}{140} \cdot 10 = \frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

Simplificar

\frac{sin ( θ )}{140} \cdot 10 : \frac{sin ( θ )}{14}

\frac{sin ( θ )}{140} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( θ ) \cdot 10}{140}

Eliminar los terminos comunes:

10

= \frac{sin ( θ )}{14}

Simplificar

\frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10 : \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( 11 0 ^{\circ} ) \cdot 10}{622}

Eliminar los terminos comunes:

2

= \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

Multiplicar ambos lados por

14

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

Multiplicar ambos lados por

14

\frac{14 sin ( θ )}{14} = \frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

Simplificar

\frac{14 sin ( θ )}{14} = \frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

Simplificar

\frac{14 sin ( θ )}{14} : sin (θ)

\frac{14 sin ( θ )}{14}

Dividir:

\frac{14}{14} = 1

= sin (θ)

Simplificar

\frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311} : \frac{70 sin ( 11 0 ^{\circ} )}{311}

\frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

Multiplicar los numeros:

14 \cdot 5 = 70

= \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

Aplicar propiedades trigonométricas inversas

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

Soluciones generales para

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

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

θ = arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n

θ = arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

θ = 0.21311 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21311 \dots + 36 0^{\circ} n

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