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Popular Trigonometría >

(sin(x))/(120)=(sin(60))/(300)

Solución

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

Solución

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

+1

Radianes

x = 0.35374 \dots + 2 πn, x = π - 0.35374 \dots + 2 πn

Pasos de solución

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

= \frac{3}{2}

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

Multiplicar ambos lados por

100

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

Multiplicar ambos lados por

100

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

Simplificar

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

Simplificar

\frac{sin ( x )}{120} \cdot 100 : \frac{5 sin ( x )}{6}

\frac{sin ( x )}{120} \cdot 100

Multiplicar fracciones:

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

= \frac{sin ( x ) \cdot 100}{120}

Eliminar los terminos comunes:

20

= \frac{5 sin ( x )}{6}

Simplificar

\frac{\frac{3}{2}}{300} \cdot 100 : \frac{3}{6}

\frac{\frac{3}{2}}{300} \cdot 100

\frac{\frac{3}{2}}{300} = \frac{3}{600}

\frac{\frac{3}{2}}{300}

Aplicar las propiedades de las fracciones:

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

= \frac{3}{2 \cdot 300}

Multiplicar los numeros:

2 \cdot 300 = 600

= \frac{3}{600}

= 100 \cdot \frac{3}{600}

Multiplicar fracciones:

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

= \frac{3 \cdot 100}{600}

Eliminar los terminos comunes:

100

= \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

Multiplicar ambos lados por

6

\frac{5 sin ( x )}{6} = \frac{3}{6}

Multiplicar ambos lados por

6

\frac{6 \cdot 5 sin ( x )}{6} = \frac{6 3}{6}

Simplificar

5 sin (x) = 3

5 sin (x) = 3

Dividir ambos lados entre

5

5 sin (x) = 3

Dividir ambos lados entre

5

\frac{5 sin ( x )}{5} = \frac{3}{5}

Simplificar

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{3}{5}

Soluciones generales para

sin (x) = \frac{3}{5}

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

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

Gráfica

Ejemplos populares

8sin(θ)+15cos(θ)=0

cos(2x-1)=sin(3x+6)

(sin(b))/(300)=(sin(49))/(500)

sin(θ)=cos(2θ+60)