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Popular Trigonometría >

5sin(pi/4 x)=4

Solución

5 sin (\frac{π}{4} x) = 4

Solución

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

Grados

x = 67.64734 \dots^{\circ} + 458.36623 \dots^{\circ} n, x = 161.53577 \dots^{\circ} + 458.36623 \dots^{\circ} n

Pasos de solución

5 sin (\frac{π}{4} x) = 4

Dividir ambos lados entre

5

5 sin (\frac{π}{4} x) = 4

Dividir ambos lados entre

5

\frac{5 sin ( \frac{π}{4} x )}{5} = \frac{4}{5}

Simplificar

sin (\frac{π}{4} x) = \frac{4}{5}

sin (\frac{π}{4} x) = \frac{4}{5}

Aplicar propiedades trigonométricas inversas

sin (\frac{π}{4} x) = \frac{4}{5}

Soluciones generales para

sin (\frac{π}{4} x) = \frac{4}{5}

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

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn, \frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn, \frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

Resolver

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

4

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

4

4 \cdot \frac{π}{4} x = 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Simplificar

4 \cdot \frac{π}{4} x = 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Simplificar

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

Multiplicar fracciones:

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

= \frac{4 π}{4} x

Eliminar los terminos comunes:

4

= x π

Simplificar

4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn : 4 arcsin (\frac{4}{5}) + 8 πn

4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Multiplicar los numeros:

4 \cdot 2 = 8

= 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

Dividir ambos lados entre

π

π x = 4 arcsin (\frac{4}{5}) + 8 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Simplificar

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

Resolver

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn : x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

4

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

4

4 \cdot \frac{π}{4} x = 4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Simplificar

4 \cdot \frac{π}{4} x = 4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Simplificar

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

Multiplicar fracciones:

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

= \frac{4 π}{4} x

Eliminar los terminos comunes:

4

= x π

Simplificar

4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn : 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Multiplicar los numeros:

4 \cdot 2 = 8

= 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

Dividir ambos lados entre

π

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Simplificar

\frac{π x}{π} = \frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π} : 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Cancelar

\frac{4 π}{π} : 4

\frac{4 π}{π}

Eliminar los terminos comunes:

π

= 4

= 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Cancelar

\frac{8 πn}{π} : 8 n

\frac{8 πn}{π}

Eliminar los terminos comunes:

π

= 8 n

= 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n, x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

Mostrar soluciones en forma decimal

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

Gráfica

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