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1/(1.5)=(sin(30))/(sin(x)),x<90

Solución

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

Solución

x = 0.84806 \dots, x = - 5.43512 \dots, x = - 18 0^{\circ} - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

radianes

x = 0.84806 \dots, x = - 5.43512 \dots, x = - π - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

Pasos de solución

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

Intercambiar lados

\frac{sin ( 3 0 ^{\circ} )}{sin ( x )} = \frac{1}{1.5}

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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{\frac{1}{2}}{sin ( x )} = \frac{1}{1.5}

Utilizar multiplicación cruzada (regla de tres)

\frac{\frac{1}{2}}{sin ( x )} = \frac{1}{1.5}

Simplificar

\frac{\frac{1}{2}}{sin ( x )} : \frac{1}{2 sin ( x )}

\frac{\frac{1}{2}}{sin ( x )}

Aplicar las propiedades de las fracciones:

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

= \frac{1}{2 sin ( x )}

\frac{1}{2 sin ( x )} = \frac{1}{1.5}

Utilizar multiplicación cruzada (regla de tres): Si

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

entonces

a \cdot d = b \cdot c

1 \cdot 1.5 = 2 sin (x) \cdot 1

Simplificar

1 \cdot 1.5 = 2 sin (x) \cdot 1

Simplificar

1 \cdot 1.5 : 1.5

1 \cdot 1.5

Multiplicar los numeros:

1 \cdot 1.5 = 1.5

= 1.5

Simplificar

2 sin (x) \cdot 1 : 2 sin (x)

2 sin (x) \cdot 1

Multiplicar los numeros:

2 \cdot 1 = 2

= 2 sin (x)

1.5 = 2 sin (x)

1.5 = 2 sin (x)

1.5 = 2 sin (x)

Intercambiar lados

2 sin (x) = 1.5

Dividir ambos lados entre

2

2 sin (x) = 1.5

Dividir ambos lados entre

2

\frac{2 sin ( x )}{2} = \frac{1.5}{2}

Simplificar

sin (x) = 0.75

sin (x) = 0.75

Verificar las soluciones

Encontrar los puntos no definidos (singularidades):

sin (x) = 0

Tomar el(los) denominador(es) de

\frac{\frac{1}{2}}{sin ( x )}

y comparar con cero

sin (x) = 0

Los siguientes puntos no están definidos

sin (x) = 0

Combinar los puntos no definidos con las soluciones:

sin (x) = 0.75

Aplicar propiedades trigonométricas inversas

sin (x) = 0.75

Soluciones generales para

sin (x) = 0.75

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

x = arcsin (0.75) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75) + 36 0^{\circ} n

x = arcsin (0.75) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75) + 36 0^{\circ} n

Soluciones para el rango

x < 9 0^{\circ}

x = 0.84806 \dots, x = - 5.43512 \dots, x = - 18 0^{\circ} - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

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cos (2 B) = \frac{21}{35}, cos (B)

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