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5sin(pi/3 x)=2

Solución

5 sin (\frac{π}{3} x) = 2

Solución

x = \frac{3 \cdot 0.41151 \dots}{π} + 6 n, x = 3 - \frac{3 \cdot 0.41151 \dots}{π} + 6 n

Grados

x = 22.51550 \dots^{\circ} + 343.77467 \dots^{\circ} n, x = 149.37183 \dots^{\circ} + 343.77467 \dots^{\circ} n

Pasos de solución

5 sin (\frac{π}{3} x) = 2

Dividir ambos lados entre

5

5 sin (\frac{π}{3} x) = 2

Dividir ambos lados entre

5

\frac{5 sin ( \frac{π}{3} x )}{5} = \frac{2}{5}

Simplificar

sin (\frac{π}{3} x) = \frac{2}{5}

sin (\frac{π}{3} x) = \frac{2}{5}

Aplicar propiedades trigonométricas inversas

sin (\frac{π}{3} x) = \frac{2}{5}

Soluciones generales para

sin (\frac{π}{3} x) = \frac{2}{5}

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

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn, \frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn, \frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn

Resolver

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn : x = \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

3

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

3

3 \cdot \frac{π}{3} x = 3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} x = 3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} x : π x

3 \cdot \frac{π}{3} x

Multiplicar fracciones:

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

= \frac{3 π}{3} x

Eliminar los terminos comunes:

3

= x π

Simplificar

3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn : 3 arcsin (\frac{2}{5}) + 6 πn

3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 3 arcsin (\frac{2}{5}) + 6 πn

π x = 3 arcsin (\frac{2}{5}) + 6 πn

π x = 3 arcsin (\frac{2}{5}) + 6 πn

π x = 3 arcsin (\frac{2}{5}) + 6 πn

Dividir ambos lados entre

π

π x = 3 arcsin (\frac{2}{5}) + 6 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{3 arcsin ( \frac{2}{5} )}{π} + \frac{6 πn}{π}

Simplificar

x = \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

x = \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

Resolver

\frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn : x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

\frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

3

\frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

3

3 \cdot \frac{π}{3} x = 3 π - 3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} x = 3 π - 3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} x : π x

3 \cdot \frac{π}{3} x

Multiplicar fracciones:

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

= \frac{3 π}{3} x

Eliminar los terminos comunes:

3

= x π

Simplificar

3 π - 3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn : 3 π - 3 arcsin (\frac{2}{5}) + 6 πn

3 π - 3 arcsin (\frac{2}{5}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 3 π - 3 arcsin (\frac{2}{5}) + 6 πn

π x = 3 π - 3 arcsin (\frac{2}{5}) + 6 πn

π x = 3 π - 3 arcsin (\frac{2}{5}) + 6 πn

π x = 3 π - 3 arcsin (\frac{2}{5}) + 6 πn

Dividir ambos lados entre

π

π x = 3 π - 3 arcsin (\frac{2}{5}) + 6 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{3 π}{π} - \frac{3 arcsin ( \frac{2}{5} )}{π} + \frac{6 πn}{π}

Simplificar

\frac{π x}{π} = \frac{3 π}{π} - \frac{3 arcsin ( \frac{2}{5} )}{π} + \frac{6 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{3 π}{π} - \frac{3 arcsin ( \frac{2}{5} )}{π} + \frac{6 πn}{π} : 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

\frac{3 π}{π} - \frac{3 arcsin ( \frac{2}{5} )}{π} + \frac{6 πn}{π}

Cancelar

\frac{3 π}{π} : 3

\frac{3 π}{π}

Eliminar los terminos comunes:

π

= 3

= 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + \frac{6 πn}{π}

Cancelar

\frac{6 πn}{π} : 6 n

\frac{6 πn}{π}

Eliminar los terminos comunes:

π

= 6 n

= 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

x = \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n, x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

Mostrar soluciones en forma decimal

x = \frac{3 \cdot 0.41151 \dots}{π} + 6 n, x = 3 - \frac{3 \cdot 0.41151 \dots}{π} + 6 n

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