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3cos(4x-26)+5=7

Solución

3 cos (4 x - 26) + 5 = 7

Solución

x = \frac{13}{2} + \frac{πn}{2} + \frac{0.84106 \dots}{4}, x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{0.84106 \dots}{4}

Grados

x = 384.46998 \dots^{\circ} + 9 0^{\circ} n, x = 450.37514 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

3 cos (4 x - 26) + 5 = 7

Mover

5

al lado derecho

3 cos (4 x - 26) + 5 = 7

Restar

5

de ambos lados

3 cos (4 x - 26) + 5 - 5 = 7 - 5

Simplificar

3 cos (4 x - 26) = 2

3 cos (4 x - 26) = 2

Dividir ambos lados entre

3

3 cos (4 x - 26) = 2

Dividir ambos lados entre

3

\frac{3 cos ( 4 x - 26 )}{3} = \frac{2}{3}

Simplificar

cos (4 x - 26) = \frac{2}{3}

cos (4 x - 26) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (4 x - 26) = \frac{2}{3}

Soluciones generales para

cos (4 x - 26) = \frac{2}{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

4 x - 26 = arccos (\frac{2}{3}) + 2 πn, 4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

4 x - 26 = arccos (\frac{2}{3}) + 2 πn, 4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

Resolver

4 x - 26 = arccos (\frac{2}{3}) + 2 πn : x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

4 x - 26 = arccos (\frac{2}{3}) + 2 πn

Mover

26

al lado derecho

4 x - 26 = arccos (\frac{2}{3}) + 2 πn

Sumar

26

a ambos lados

4 x - 26 + 26 = arccos (\frac{2}{3}) + 2 πn + 26

Simplificar

4 x = arccos (\frac{2}{3}) + 2 πn + 26

4 x = arccos (\frac{2}{3}) + 2 πn + 26

Dividir ambos lados entre

4

4 x = arccos (\frac{2}{3}) + 2 πn + 26

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplificar

\frac{4 x}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4} : \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

\frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Agrupar términos semejantes

= \frac{26}{4} + \frac{2 πn}{4} + \frac{arccos ( \frac{2}{3} )}{4}

Cancelar

\frac{26}{4} : \frac{13}{2}

\frac{26}{4}

Eliminar los terminos comunes:

2

= \frac{13}{2}

= \frac{13}{2} + \frac{2 πn}{4} + \frac{arccos ( \frac{2}{3} )}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

Resolver

4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn : x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

Mover

26

al lado derecho

4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

Sumar

26

a ambos lados

4 x - 26 + 26 = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

Simplificar

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

Dividir ambos lados entre

4

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplificar

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4} : \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

\frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Agrupar términos semejantes

= \frac{2 π}{4} + \frac{26}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{2}{3} )}{4}

Cancelar

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Eliminar los terminos comunes:

2

= \frac{π}{2}

= \frac{π}{2} + \frac{26}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{2}{3} )}{4}

Cancelar

\frac{26}{4} : \frac{13}{2}

\frac{26}{4}

Eliminar los terminos comunes:

2

= \frac{13}{2}

= \frac{π}{2} + \frac{13}{2} + \frac{2 πn}{4} - \frac{arccos ( \frac{2}{3} )}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}, x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

Mostrar soluciones en forma decimal

x = \frac{13}{2} + \frac{πn}{2} + \frac{0.84106 \dots}{4}, x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{0.84106 \dots}{4}

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