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3cos(2x+1)=2

Solución

3 cos (2 x + 1) = 2

Solución

x = πn - \frac{1}{2} + \frac{0.84106 \dots}{2}, x = π + πn - \frac{1}{2} - \frac{0.84106 \dots}{2}

Grados

x = - 4.55304 \dots^{\circ} + 18 0^{\circ} n, x = 127.25726 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

3 cos (2 x + 1) = 2

Dividir ambos lados entre

3

3 cos (2 x + 1) = 2

Dividir ambos lados entre

3

\frac{3 cos ( 2 x + 1 )}{3} = \frac{2}{3}

Simplificar

cos (2 x + 1) = \frac{2}{3}

cos (2 x + 1) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (2 x + 1) = \frac{2}{3}

Soluciones generales para

cos (2 x + 1) = \frac{2}{3}

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

2 x + 1 = arccos (\frac{2}{3}) + 2 πn, 2 x + 1 = 2 π - arccos (\frac{2}{3}) + 2 πn

2 x + 1 = arccos (\frac{2}{3}) + 2 πn, 2 x + 1 = 2 π - arccos (\frac{2}{3}) + 2 πn

Resolver

2 x + 1 = arccos (\frac{2}{3}) + 2 πn : x = πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}

2 x + 1 = arccos (\frac{2}{3}) + 2 πn

Mover

1

al lado derecho

2 x + 1 = arccos (\frac{2}{3}) + 2 πn

Restar

1

de ambos lados

2 x + 1 - 1 = arccos (\frac{2}{3}) + 2 πn - 1

Simplificar

2 x = arccos (\frac{2}{3}) + 2 πn - 1

2 x = arccos (\frac{2}{3}) + 2 πn - 1

Dividir ambos lados entre

2

2 x = arccos (\frac{2}{3}) + 2 πn - 1

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2}

Simplificar

\frac{2 x}{2} = \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2} : πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}

\frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2}

Agrupar términos semejantes

= - \frac{1}{2} + \frac{2 πn}{2} + \frac{arccos ( \frac{2}{3} )}{2}

Dividir:

\frac{2}{2} = 1

= - \frac{1}{2} + πn + \frac{arccos ( \frac{2}{3} )}{2}

Agrupar términos semejantes

= πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}

x = πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}

x = πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}

x = πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}

Resolver

2 x + 1 = 2 π - arccos (\frac{2}{3}) + 2 πn : x = π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

2 x + 1 = 2 π - arccos (\frac{2}{3}) + 2 πn

Mover

1

al lado derecho

2 x + 1 = 2 π - arccos (\frac{2}{3}) + 2 πn

Restar

1

de ambos lados

2 x + 1 - 1 = 2 π - arccos (\frac{2}{3}) + 2 πn - 1

Simplificar

2 x = 2 π - arccos (\frac{2}{3}) + 2 πn - 1

2 x = 2 π - arccos (\frac{2}{3}) + 2 πn - 1

Dividir ambos lados entre

2

2 x = 2 π - arccos (\frac{2}{3}) + 2 πn - 1

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2}

Simplificar

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{2 π}{2} - \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2} : π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

\frac{2 π}{2} - \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2} - \frac{1}{2}

Agrupar términos semejantes

= - \frac{1}{2} + \frac{2 π}{2} + \frac{2 πn}{2} - \frac{arccos ( \frac{2}{3} )}{2}

Dividir:

\frac{2}{2} = 1

= - \frac{1}{2} + π + πn - \frac{arccos ( \frac{2}{3} )}{2}

Agrupar términos semejantes

= π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

x = π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

x = π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

x = π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

x = πn - \frac{1}{2} + \frac{arccos ( \frac{2}{3} )}{2}, x = π + πn - \frac{1}{2} - \frac{arccos ( \frac{2}{3} )}{2}

Mostrar soluciones en forma decimal

x = πn - \frac{1}{2} + \frac{0.84106 \dots}{2}, x = π + πn - \frac{1}{2} - \frac{0.84106 \dots}{2}

Ejemplos populares

sin(t)= 3/7 ,cos(t)

sin (t) = \frac{3}{7}, cos (t)

tan(x)= 16/12

tan (x) = \frac{16}{12}

sin(4x+10)=sin(90)

sin (4 x + 10) = sin (9 0^{\circ})

solvefor y,-1/2 cot(y)=(t^2)/(+2)+C resolver para

y, - \frac{1}{2} cot (y) = \frac{t ^{2}}{+ 2} + C

sqrt(3)sec(2θ)+2=0

3 sec (2 θ) + 2 = 0