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Popular Trigonometría >

(sin(θ))/(60)=(sin(45))/(246.26)

Solución

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

Solución

θ = 0.17314 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17314 \dots + 36 0^{\circ} n

Radianes

θ = 0.17314 \dots + 2 πn, θ = π - 0.17314 \dots + 2 πn

Pasos de solución

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

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

sin (4 5^{\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}

= \frac{2}{2}

\frac{sin ( θ )}{60} = \frac{\frac{2}{2}}{246.26}

Multiplicar ambos lados por

10

\frac{sin ( θ )}{60} = \frac{\frac{2}{2}}{246.26}

Multiplicar ambos lados por

10

\frac{sin ( θ )}{60} \cdot 10 = \frac{\frac{2}{2}}{246.26} \cdot 10

Simplificar

\frac{sin ( θ )}{60} \cdot 10 = \frac{\frac{2}{2}}{246.26} \cdot 10

Simplificar

\frac{sin ( θ )}{60} \cdot 10 : \frac{sin ( θ )}{6}

\frac{sin ( θ )}{60} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( θ ) \cdot 10}{60}

Eliminar los terminos comunes:

10

= \frac{sin ( θ )}{6}

Simplificar

\frac{\frac{2}{2}}{246.26} \cdot 10 : \frac{10 2}{492.52}

\frac{\frac{2}{2}}{246.26} \cdot 10

\frac{\frac{2}{2}}{246.26} = \frac{2}{492.52}

\frac{\frac{2}{2}}{246.26}

Aplicar las propiedades de las fracciones:

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

= \frac{2}{2 \cdot 246.26}

Multiplicar los numeros:

2 \cdot 246.26 = 492.52

= \frac{2}{492.52}

= 10 \cdot \frac{2}{492.52}

Multiplicar fracciones:

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

= \frac{2 \cdot 10}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

Multiplicar ambos lados por

6

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

Multiplicar ambos lados por

6

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 2}{492.52}

Simplificar

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 2}{492.52}

Simplificar

\frac{6 sin ( θ )}{6} : sin (θ)

\frac{6 sin ( θ )}{6}

Dividir:

\frac{6}{6} = 1

= sin (θ)

Simplificar

\frac{6 \cdot 10 2}{492.52} : 0.17228 \dots

\frac{6 \cdot 10 2}{492.52}

Multiplicar los numeros:

6 \cdot 10 = 60

= \frac{60 2}{492.52}

Convertir el elemento a una forma decimal

2 = 1.41421 \dots

= \frac{60 \cdot 1.41421 \dots}{492.52}

Multiplicar los numeros:

60 \cdot 1.41421 \dots = 84.85281 \dots

= \frac{84.85281 \dots}{492.52}

Dividir:

\frac{84.85281 \dots}{492.52} = 0.17228 \dots

= 0.17228 \dots

sin (θ) = 0.17228 \dots

sin (θ) = 0.17228 \dots

sin (θ) = 0.17228 \dots

Aplicar propiedades trigonométricas inversas

sin (θ) = 0.17228 \dots

Soluciones generales para

sin (θ) = 0.17228 \dots

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

θ = arcsin (0.17228 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.17228 \dots) + 36 0^{\circ} n

θ = arcsin (0.17228 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.17228 \dots) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

θ = 0.17314 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17314 \dots + 36 0^{\circ} n

Gráfica

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