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(sin(115))/(20)=(sin(B))/(15)

Solución

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

B = 0.74739 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.74739 \dots + 36 0^{\circ} n

radianes

B = 0.74739 \dots + 2 πn, B = π - 0.74739 \dots + 2 πn

Pasos de solución

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

Intercambiar lados

\frac{sin ( B )}{15} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiplicar ambos lados por

10

\frac{sin ( B )}{15} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiplicar ambos lados por

10

\frac{sin ( B )}{15} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplificar

\frac{sin ( B )}{15} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplificar

\frac{sin ( B )}{15} \cdot 10 : \frac{2 sin ( B )}{3}

\frac{sin ( B )}{15} \cdot 10

Multiplicar fracciones:

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

= \frac{sin ( B ) \cdot 10}{15}

Eliminar los terminos comunes:

5

= \frac{2 sin ( B )}{3}

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{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiplicar ambos lados por

3

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiplicar ambos lados por

3

\frac{3 \cdot 2 sin ( B )}{3} = \frac{3 sin ( 11 5 ^{\circ} )}{2}

Simplificar

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

Dividir ambos lados entre

2

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

Dividir ambos lados entre

2

\frac{2 sin ( B )}{2} = \frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

Simplificar

\frac{2 sin ( B )}{2} = \frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

Simplificar

\frac{2 sin ( B )}{2} : sin (B)

\frac{2 sin ( B )}{2}

Dividir:

\frac{2}{2} = 1

= sin (B)

Simplificar

\frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2} : \frac{3 sin ( 11 5 ^{\circ} )}{4}

\frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{3 sin ( 11 5 ^{\circ} )}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

Aplicar propiedades trigonométricas inversas

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

Soluciones generales para

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

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

B = arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n

B = arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

B = 0.74739 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.74739 \dots + 36 0^{\circ} n

3 tan (θ) + 1 = 2 tan (θ)

cos (x) = \frac{18}{25}

sin (x) = - \frac{2}{2}, - π \leq x \leq π

w, s (t) = A e^{- c t} cos (wt + b)

0 = 2 sin (t) + cos (2 t)