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cos(2/3 x-pi/2)=1

Solución

cos (\frac{2}{3} x - \frac{π}{2}) = 1

Solución

x = 3 πn + \frac{3 π}{4}

+1

Grados

x = 13 5^{\circ} + 54 0^{\circ} n

Pasos de solución

cos (\frac{2}{3} x - \frac{π}{2}) = 1

Soluciones generales para

cos (\frac{2}{3} x - \frac{π}{2}) = 1

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{2}{3} x - \frac{π}{2} = 0 + 2 πn

\frac{2}{3} x - \frac{π}{2} = 0 + 2 πn

Resolver

\frac{2}{3} x - \frac{π}{2} = 0 + 2 πn : x = 3 πn + \frac{3 π}{4}

\frac{2}{3} x - \frac{π}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{2}{3} x - \frac{π}{2} = 2 πn

Mover

\frac{π}{2}

al lado derecho

\frac{2}{3} x - \frac{π}{2} = 2 πn

Sumar

\frac{π}{2}

a ambos lados

\frac{2}{3} x - \frac{π}{2} + \frac{π}{2} = 2 πn + \frac{π}{2}

Simplificar

\frac{2}{3} x = 2 πn + \frac{π}{2}

\frac{2}{3} x = 2 πn + \frac{π}{2}

Multiplicar ambos lados por

3

\frac{2}{3} x = 2 πn + \frac{π}{2}

Multiplicar ambos lados por

3

3 \cdot \frac{2}{3} x = 3 \cdot 2 πn + 3 \cdot \frac{π}{2}

Simplificar

3 \cdot \frac{2}{3} x = 3 \cdot 2 πn + 3 \cdot \frac{π}{2}

Simplificar

3 \cdot \frac{2}{3} x : 2 x

3 \cdot \frac{2}{3} x

Multiplicar fracciones:

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

= \frac{2 \cdot 3}{3} x

Eliminar los terminos comunes:

3

= x \cdot 2

Simplificar

3 \cdot 2 πn + 3 \cdot \frac{π}{2} : 6 πn + \frac{3 π}{2}

3 \cdot 2 πn + 3 \cdot \frac{π}{2}

Multiplicar los numeros:

3 \cdot 2 = 6

= 6 πn + 3 \cdot \frac{π}{2}

Multiplicar

3 \cdot \frac{π}{2} : \frac{3 π}{2}

3 \cdot \frac{π}{2}

Multiplicar fracciones:

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

= \frac{π 3}{2}

= 6 πn + \frac{3 π}{2}

2 x = 6 πn + \frac{3 π}{2}

2 x = 6 πn + \frac{3 π}{2}

2 x = 6 πn + \frac{3 π}{2}

Dividir ambos lados entre

2

2 x = 6 πn + \frac{3 π}{2}

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{6 πn}{2} + \frac{\frac{3 π}{2}}{2}

Simplificar

\frac{2 x}{2} = \frac{6 πn}{2} + \frac{\frac{3 π}{2}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{6 πn}{2} + \frac{\frac{3 π}{2}}{2} : 3 πn + \frac{3 π}{4}

\frac{6 πn}{2} + \frac{\frac{3 π}{2}}{2}

\frac{6 πn}{2} = 3 πn

\frac{6 πn}{2}

Dividir:

\frac{6}{2} = 3

= 3 πn

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{3 π}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{3 π}{4}

= 3 πn + \frac{3 π}{4}

x = 3 πn + \frac{3 π}{4}

x = 3 πn + \frac{3 π}{4}

x = 3 πn + \frac{3 π}{4}

x = 3 πn + \frac{3 π}{4}

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