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(sin(1.3785)}{70}=\frac{sin(a))/7

Solución

\frac{sin ( 1.3785 )}{70} = \frac{sin ( a )}{7}

a = 0.09831 \dots + 2 πn, a = π - 0.09831 \dots + 2 πn

Grados

a = 5.63304 \dots^{\circ} + 36 0^{\circ} n, a = 174.36695 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{sin ( 1.3785 )}{70} = \frac{sin ( a )}{7}

sin (1.3785) = sin (\frac{2757}{2000})

sin (1.3785)

\frac{sin ( \frac{2757}{2000} )}{70} = \frac{sin ( a )}{7}

Intercambiar lados

\frac{sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{70}

Multiplicar ambos lados por

10

\frac{sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{70}

Multiplicar ambos lados por

10

\frac{sin ( a )}{7} \cdot 10 = \frac{sin ( \frac{2757}{2000} )}{70} \cdot 10

Simplificar

\frac{sin ( a )}{7} \cdot 10 = \frac{sin ( \frac{2757}{2000} )}{70} \cdot 10

Simplificar

\frac{sin ( a )}{7} \cdot 10 : \frac{10 sin ( a )}{7}

\frac{sin ( a )}{7} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( a ) \cdot 10}{7}

Simplificar

\frac{sin ( \frac{2757}{2000} )}{70} \cdot 10 : \frac{sin ( \frac{2757}{2000} )}{7}

\frac{sin ( \frac{2757}{2000} )}{70} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( \frac{2757}{2000} ) \cdot 10}{70}

Eliminar los terminos comunes:

10

= \frac{sin ( \frac{2757}{2000} )}{7}

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

Multiplicar ambos lados por

7

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

Multiplicar ambos lados por

7

\frac{7 \cdot 10 sin ( a )}{7} = \frac{7 sin ( \frac{2757}{2000} )}{7}

Simplificar

10 sin (a) = sin (\frac{2757}{2000})

10 sin (a) = sin (\frac{2757}{2000})

Dividir ambos lados entre

10

10 sin (a) = sin (\frac{2757}{2000})

Dividir ambos lados entre

10

\frac{10 sin ( a )}{10} = \frac{sin ( \frac{2757}{2000} )}{10}

Simplificar

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

Aplicar propiedades trigonométricas inversas

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

Soluciones generales para

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

a = arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn, a = π - arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn

a = arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn, a = π - arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn

Mostrar soluciones en forma decimal

a = 0.09831 \dots + 2 πn, a = π - 0.09831 \dots + 2 πn