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(sin(115))/(20)=(sin(b))/(11)

Solución

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

b = 0.52183 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.52183 \dots + 36 0^{\circ} n

radianes

b = 0.52183 \dots + 2 πn, b = π - 0.52183 \dots + 2 πn

Pasos de solución

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

Intercambiar lados

\frac{sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiplicar ambos lados por

10

\frac{sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiplicar ambos lados por

10

\frac{sin ( b )}{11} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplificar

\frac{sin ( b )}{11} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplificar

\frac{sin ( b )}{11} \cdot 10 : \frac{10 sin ( b )}{11}

\frac{sin ( b )}{11} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( b ) \cdot 10}{11}

Simplificar

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10 : \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( 11 5 ^{\circ} ) \cdot 10}{20}

Eliminar los terminos comunes:

10

= \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiplicar ambos lados por

11

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiplicar ambos lados por

11

\frac{11 \cdot 10 sin ( b )}{11} = \frac{11 sin ( 11 5 ^{\circ} )}{2}

Simplificar

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

Dividir ambos lados entre

10

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

Dividir ambos lados entre

10

\frac{10 sin ( b )}{10} = \frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

Simplificar

\frac{10 sin ( b )}{10} = \frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

Simplificar

\frac{10 sin ( b )}{10} : sin (b)

\frac{10 sin ( b )}{10}

Dividir:

\frac{10}{10} = 1

= sin (b)

Simplificar

\frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10} : \frac{11 sin ( 11 5 ^{\circ} )}{20}

\frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

Aplicar las propiedades de las fracciones:

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

= \frac{11 sin ( 11 5 ^{\circ} )}{2 \cdot 10}

Multiplicar los numeros:

2 \cdot 10 = 20

= \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

Aplicar propiedades trigonométricas inversas

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

Soluciones generales para

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

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

b = arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n

b = arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

b = 0.52183 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.52183 \dots + 36 0^{\circ} n

y, \frac{sin ( 7 y )}{7} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

3 cos (\frac{π x}{12}) + 8.4 = 7

sin (x) = \frac{1}{6}, tan (x)

2 sin^{2} (x) + sin (x) - 2 = 0

cos (θ) = \frac{25}{714}