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Popular >

cos(2θ-pi/2)=-1,0<= θ<= 2pi

Solución

cos (2 θ - \frac{π}{2}) = - 1, 0 \leq θ \leq 2 π

Solución

θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

+1

Grados

θ = 13 5^{\circ}, θ = 31 5^{\circ}

Pasos de solución

cos (2 θ - \frac{π}{2}) = - 1, 0 \leq θ \leq 2 π

Soluciones generales para

cos (2 θ - \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}

2 θ - \frac{π}{2} = π + 2 πn

2 θ - \frac{π}{2} = π + 2 πn

Resolver

2 θ - \frac{π}{2} = π + 2 πn : θ = πn + \frac{π}{2} + \frac{π}{4}

2 θ - \frac{π}{2} = π + 2 πn

Mover

\frac{π}{2}

al lado derecho

2 θ - \frac{π}{2} = π + 2 πn

Sumar

\frac{π}{2}

a ambos lados

2 θ - \frac{π}{2} + \frac{π}{2} = π + 2 πn + \frac{π}{2}

Simplificar

2 θ = π + 2 πn + \frac{π}{2}

2 θ = π + 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

2 θ = π + 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Simplificar

\frac{2 θ}{2} = \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

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

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{π}{4}

= \frac{π}{2} + πn + \frac{π}{4}

Agrupar términos semejantes

= πn + \frac{π}{2} + \frac{π}{4}

θ = πn + \frac{π}{2} + \frac{π}{4}

θ = πn + \frac{π}{2} + \frac{π}{4}

θ = πn + \frac{π}{2} + \frac{π}{4}

θ = πn + \frac{π}{2} + \frac{π}{4}

Soluciones para el rango

0 \leq θ \leq 2 π

θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

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