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Popular Trigonometría >

(sin(90))/(458.912)=(sin(x))/(450)

Solución

\frac{sin ( 9 0 ^{\circ} )}{458.912} = \frac{sin ( x )}{450}

Solución

x = 1.37339 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.37339 \dots + 36 0^{\circ} n

+1

Radianes

x = 1.37339 \dots + 2 πn, x = π - 1.37339 \dots + 2 πn

Pasos de solución

\frac{sin ( 9 0 ^{\circ} )}{458.912} = \frac{sin ( x )}{450}

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

= 1

\frac{1}{458.912} = \frac{sin ( x )}{450}

Intercambiar lados

\frac{sin ( x )}{450} = \frac{1}{458.912}

Multiplicar ambos lados por

10

\frac{sin ( x )}{450} = \frac{1}{458.912}

Multiplicar ambos lados por

10

\frac{sin ( x )}{450} \cdot 10 = \frac{1}{458.912} \cdot 10

Simplificar

\frac{sin ( x )}{450} \cdot 10 = \frac{1}{458.912} \cdot 10

Simplificar

\frac{sin ( x )}{450} \cdot 10 : \frac{sin ( x )}{45}

\frac{sin ( x )}{450} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( x ) \cdot 10}{450}

Eliminar los terminos comunes:

10

= \frac{sin ( x )}{45}

Simplificar

\frac{1}{458.912} \cdot 10 : \frac{10}{458.912}

\frac{1}{458.912} \cdot 10

Multiplicar fracciones:

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

= \frac{1 \cdot 10}{458.912}

Multiplicar los numeros:

1 \cdot 10 = 10

= \frac{10}{458.912}

\frac{sin ( x )}{45} = \frac{10}{458.912}

\frac{sin ( x )}{45} = \frac{10}{458.912}

\frac{sin ( x )}{45} = \frac{10}{458.912}

Multiplicar ambos lados por

45

\frac{sin ( x )}{45} = \frac{10}{458.912}

Multiplicar ambos lados por

45

\frac{45 sin ( x )}{45} = \frac{10 \cdot 45}{458.912}

Simplificar

\frac{45 sin ( x )}{45} = \frac{10 \cdot 45}{458.912}

Simplificar

\frac{45 sin ( x )}{45} : sin (x)

\frac{45 sin ( x )}{45}

Dividir:

\frac{45}{45} = 1

= sin (x)

Simplificar

\frac{10 \cdot 45}{458.912} : 0.98058 \dots

\frac{10 \cdot 45}{458.912}

Multiplicar los numeros:

10 \cdot 45 = 450

= \frac{450}{458.912}

Dividir:

\frac{450}{458.912} = 0.98058 \dots

= 0.98058 \dots

sin (x) = 0.98058 \dots

sin (x) = 0.98058 \dots

sin (x) = 0.98058 \dots

Aplicar propiedades trigonométricas inversas

sin (x) = 0.98058 \dots

Soluciones generales para

sin (x) = 0.98058 \dots

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

x = arcsin (0.98058 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.98058 \dots) + 36 0^{\circ} n

x = arcsin (0.98058 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.98058 \dots) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

x = 1.37339 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.37339 \dots + 36 0^{\circ} n

Gráfica

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