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Popular Trigonometría >

(sin(θ))/(20)=(sin(150))/(58.1826)

Solución

\frac{sin ( θ )}{20} = \frac{sin ( 15 0 ^{\circ} )}{58.1826}

Solución

θ = 0.17273 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17273 \dots + 36 0^{\circ} n

Radianes

θ = 0.17273 \dots + 2 πn, θ = π - 0.17273 \dots + 2 πn

Pasos de solución

\frac{sin ( θ )}{20} = \frac{sin ( 15 0 ^{\circ} )}{58.1826}

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

sin (15 0^{\circ})

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}

= \frac{1}{2}

\frac{sin ( θ )}{20} = \frac{\frac{1}{2}}{58.1826}

Multiplicar ambos lados por

10

\frac{sin ( θ )}{20} = \frac{\frac{1}{2}}{58.1826}

Multiplicar ambos lados por

10

\frac{sin ( θ )}{20} \cdot 10 = \frac{\frac{1}{2}}{58.1826} \cdot 10

Simplificar

\frac{sin ( θ )}{20} \cdot 10 = \frac{\frac{1}{2}}{58.1826} \cdot 10

Simplificar

\frac{sin ( θ )}{20} \cdot 10 : \frac{sin ( θ )}{2}

\frac{sin ( θ )}{20} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( θ ) \cdot 10}{20}

Eliminar los terminos comunes:

10

= \frac{sin ( θ )}{2}

Simplificar

\frac{\frac{1}{2}}{58.1826} \cdot 10 : \frac{10}{116.3652}

\frac{\frac{1}{2}}{58.1826} \cdot 10

\frac{\frac{1}{2}}{58.1826} = \frac{1}{116.3652}

\frac{\frac{1}{2}}{58.1826}

Aplicar las propiedades de las fracciones:

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

= \frac{1}{2 \cdot 58.1826}

Multiplicar los numeros:

2 \cdot 58.1826 = 116.3652

= \frac{1}{116.3652}

= 10 \cdot \frac{1}{116.3652}

Multiplicar fracciones:

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

= \frac{1 \cdot 10}{116.3652}

Multiplicar los numeros:

1 \cdot 10 = 10

= \frac{10}{116.3652}

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

Multiplicar ambos lados por

2

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

Multiplicar ambos lados por

2

\frac{2 sin ( θ )}{2} = \frac{10 \cdot 2}{116.3652}

Simplificar

\frac{2 sin ( θ )}{2} = \frac{10 \cdot 2}{116.3652}

Simplificar

\frac{2 sin ( θ )}{2} : sin (θ)

\frac{2 sin ( θ )}{2}

Dividir:

\frac{2}{2} = 1

= sin (θ)

Simplificar

\frac{10 \cdot 2}{116.3652} : \frac{20}{116.3652}

\frac{10 \cdot 2}{116.3652}

Multiplicar los numeros:

10 \cdot 2 = 20

= \frac{20}{116.3652}

sin (θ) = \frac{20}{116.3652}

sin (θ) = \frac{20}{116.3652}

sin (θ) = \frac{20}{116.3652}

Aplicar propiedades trigonométricas inversas

sin (θ) = \frac{20}{116.3652}

Soluciones generales para

sin (θ) = \frac{20}{116.3652}

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

θ = arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n

θ = arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

θ = 0.17273 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17273 \dots + 36 0^{\circ} n

Gráfica

Ejemplos populares

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