English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometría >

3sin(pi/5 x)=2

Solución

3 sin (\frac{π}{5} x) = 2

Solución

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

Grados

x = 66.54318 \dots^{\circ} + 572.95779 \dots^{\circ} n, x = 219.93571 \dots^{\circ} + 572.95779 \dots^{\circ} n

Pasos de solución

3 sin (\frac{π}{5} x) = 2

Dividir ambos lados entre

3

3 sin (\frac{π}{5} x) = 2

Dividir ambos lados entre

3

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

Simplificar

sin (\frac{π}{5} x) = \frac{2}{3}

sin (\frac{π}{5} x) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

sin (\frac{π}{5} x) = \frac{2}{3}

Soluciones generales para

sin (\frac{π}{5} x) = \frac{2}{3}

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

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

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

Resolver

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

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

Multiplicar ambos lados por

5

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

Multiplicar ambos lados por

5

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

Simplificar

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

Simplificar

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

Multiplicar fracciones:

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

= \frac{5 π}{5} x

Eliminar los terminos comunes:

5

= x π

Simplificar

5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn : 5 arcsin (\frac{2}{3}) + 10 πn

5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

Dividir ambos lados entre

π

π x = 5 arcsin (\frac{2}{3}) + 10 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Simplificar

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

Resolver

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn : x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

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

Multiplicar ambos lados por

5

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

Multiplicar ambos lados por

5

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

Simplificar

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

Simplificar

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

Multiplicar fracciones:

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

= \frac{5 π}{5} x

Eliminar los terminos comunes:

5

= x π

Simplificar

5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn : 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

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

Multiplicar los numeros:

5 \cdot 2 = 10

= 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

Dividir ambos lados entre

π

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Simplificar

\frac{π x}{π} = \frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π} : 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Cancelar

\frac{5 π}{π} : 5

\frac{5 π}{π}

Eliminar los terminos comunes:

π

= 5

= 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Cancelar

\frac{10 πn}{π} : 10 n

\frac{10 πn}{π}

Eliminar los terminos comunes:

π

= 10 n

= 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n, x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

Mostrar soluciones en forma decimal

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

Gráfica

Ejemplos populares

2sin(x)=csc(x)-6,0<= x<2pi