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Popular >

0.06=0.1*cos(4x-1.57)

Solución

0.06 = 0.1 \cdot cos (4 x - 1.57)

Solución

x = \frac{1.57}{4} + \frac{πn}{2} + \frac{0.92729 \dots}{4}, x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{0.92729 \dots}{4}

Grados

x = 35.77111 \dots^{\circ} + 9 0^{\circ} n, x = 99.20606 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

0.06 = 0.1 cos (4 x - 1.57)

Intercambiar lados

0.1 cos (4 x - 1.57) = 0.06

Multiplicar ambos lados por

100

0.1 cos (4 x - 1.57) = 0.06

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

0.1 cos (4 x - 1.57) \cdot 100 = 0.06 \cdot 100

Simplificar

10 cos (4 x - 1.57) = 6

10 cos (4 x - 1.57) = 6

Dividir ambos lados entre

10

10 cos (4 x - 1.57) = 6

Dividir ambos lados entre

10

\frac{10 cos ( 4 x - 1.57 )}{10} = \frac{6}{10}

Simplificar

cos (4 x - 1.57) = \frac{3}{5}

cos (4 x - 1.57) = \frac{3}{5}

Aplicar propiedades trigonométricas inversas

cos (4 x - 1.57) = \frac{3}{5}

Soluciones generales para

cos (4 x - 1.57) = \frac{3}{5}

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

4 x - 1.57 = arccos (\frac{3}{5}) + 2 πn, 4 x - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

4 x - 1.57 = arccos (\frac{3}{5}) + 2 πn, 4 x - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

Resolver

4 x - 1.57 = arccos (\frac{3}{5}) + 2 πn : x = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

4 x - 1.57 = arccos (\frac{3}{5}) + 2 πn

Mover

1.57

al lado derecho

4 x - 1.57 = arccos (\frac{3}{5}) + 2 πn

Sumar

1.57

a ambos lados

4 x - 1.57 + 1.57 = arccos (\frac{3}{5}) + 2 πn + 1.57

Simplificar

4 x = arccos (\frac{3}{5}) + 2 πn + 1.57

4 x = arccos (\frac{3}{5}) + 2 πn + 1.57

Dividir ambos lados entre

4

4 x = arccos (\frac{3}{5}) + 2 πn + 1.57

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplificar

\frac{4 x}{4} = \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4} : \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

\frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Agrupar términos semejantes

= \frac{1.57}{4} + \frac{2 πn}{4} + \frac{arccos ( \frac{3}{5} )}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

Resolver

4 x - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn : x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

4 x - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

Mover

1.57

al lado derecho

4 x - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

Sumar

1.57

a ambos lados

4 x - 1.57 + 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

Simplificar

4 x = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

4 x = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

Dividir ambos lados entre

4

4 x = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplificar

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{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{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4} : \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Agrupar términos semejantes

= \frac{2 π}{4} + \frac{1.57}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{3}{5} )}{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{1.57}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{3}{5} )}{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{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

x = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}, x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

Mostrar soluciones en forma decimal

x = \frac{1.57}{4} + \frac{πn}{2} + \frac{0.92729 \dots}{4}, x = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{0.92729 \dots}{4}

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