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Popular Trigonometría >

5cos(3x+60)=4

Solución

5 cos (3 x + 60) = 4

Solución

x = - 20 + \frac{2 πn}{3} + \frac{0.64350 \dots}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{0.64350 \dots}{3} - 20

Grados

x = - 1133.62562 \dots^{\circ} + 12 0^{\circ} n, x = - 1038.20555 \dots^{\circ} + 12 0^{\circ} n

Pasos de solución

5 cos (3 x + 60) = 4

Dividir ambos lados entre

5

5 cos (3 x + 60) = 4

Dividir ambos lados entre

5

\frac{5 cos ( 3 x + 60 )}{5} = \frac{4}{5}

Simplificar

cos (3 x + 60) = \frac{4}{5}

cos (3 x + 60) = \frac{4}{5}

Aplicar propiedades trigonométricas inversas

cos (3 x + 60) = \frac{4}{5}

Soluciones generales para

cos (3 x + 60) = \frac{4}{5}

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

3 x + 60 = arccos (\frac{4}{5}) + 2 πn, 3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

3 x + 60 = arccos (\frac{4}{5}) + 2 πn, 3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

Resolver

3 x + 60 = arccos (\frac{4}{5}) + 2 πn : x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

3 x + 60 = arccos (\frac{4}{5}) + 2 πn

Desplace

60

a la derecha

3 x + 60 = arccos (\frac{4}{5}) + 2 πn

Restar

60

de ambos lados

3 x + 60 - 60 = arccos (\frac{4}{5}) + 2 πn - 60

Simplificar

3 x = arccos (\frac{4}{5}) + 2 πn - 60

3 x = arccos (\frac{4}{5}) + 2 πn - 60

Dividir ambos lados entre

3

3 x = arccos (\frac{4}{5}) + 2 πn - 60

Dividir ambos lados entre

3

\frac{3 x}{3} = \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

Simplificar

\frac{3 x}{3} = \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3} : - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

\frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

Agrupar términos semejantes

= - \frac{60}{3} + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

Dividir:

\frac{60}{3} = 20

= - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

Resolver

3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn : x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

Desplace

60

a la derecha

3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

Restar

60

de ambos lados

3 x + 60 - 60 = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

Simplificar

3 x = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

3 x = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

Dividir ambos lados entre

3

3 x = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

Dividir ambos lados entre

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

Simplificar

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3} : \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

\frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

Agrupar términos semejantes

= \frac{2 π}{3} - \frac{60}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3}

Dividir:

\frac{60}{3} = 20

= \frac{2 π}{3} - 20 + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3}

Agrupar términos semejantes

= \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

Mostrar soluciones en forma decimal

x = - 20 + \frac{2 πn}{3} + \frac{0.64350 \dots}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{0.64350 \dots}{3} - 20

Gráfica

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