es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(2θ-pi/2)=1

Solución

cos (2 θ - \frac{π}{2}) = 1

Solución

θ = πn + \frac{π}{4}

+1

Grados

θ = 4 5^{\circ} + 18 0^{\circ} n

Pasos de solución

cos (2 θ - \frac{π}{2}) = 1

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} = 0 + 2 πn

2 θ - \frac{π}{2} = 0 + 2 πn

Resolver

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

2 θ - \frac{π}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

2 θ - \frac{π}{2} = 2 πn

Mover

\frac{π}{2}

al lado derecho

2 θ - \frac{π}{2} = 2 πn

Sumar

\frac{π}{2}

a ambos lados

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

Simplificar

2 θ = 2 πn + \frac{π}{2}

2 θ = 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

2 θ = 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

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

Simplificar

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

\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}

= πn + \frac{π}{4}

θ = πn + \frac{π}{4}

θ = πn + \frac{π}{4}

θ = πn + \frac{π}{4}

θ = πn + \frac{π}{4}

Ejemplos populares

-sin(2x)+cos(x)=0

- sin (2 x) + cos (x) = 0

3 csc^{2} (x) = 4

6sec^2(x)+3tan^2(x)-9=0

6 sec^{2} (x) + 3 tan^{2} (x) - 9 = 0

(3tan^2(x)-1)(tan^2(x)-3)=0

(3 tan^{2} (x) - 1) (tan^{2} (x) - 3) = 0

tan(2x)=-tan(x)

tan (2 x) = - tan (x)