es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(x)= 1/2+1/2 cos^2(x)

Solución

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

Solución

x = 2 πn, x = π + 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Usando el método de sustitución

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

Sea:

cos (x) = u

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2}

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2} : u = 1, u = - 1

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2}

Mover

\frac{1}{2} u^{2}

al lado izquierdo

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2}

Restar

\frac{1}{2} u^{2}

de ambos lados

u^{2} - \frac{1}{2} u^{2} = \frac{1}{2} + \frac{1}{2} u^{2} - \frac{1}{2} u^{2}

Simplificar

\frac{1}{2} u^{2} = \frac{1}{2}

\frac{1}{2} u^{2} = \frac{1}{2}

Multiplicar ambos lados por

2

\frac{1}{2} u^{2} = \frac{1}{2}

Multiplicar ambos lados por

2

2 \cdot \frac{1}{2} u^{2} = \frac{1 \cdot 2}{2}

Simplificar

2 \cdot \frac{1}{2} u^{2} = \frac{1 \cdot 2}{2}

Simplificar

2 \cdot \frac{1}{2} u^{2} : u^{2}

2 \cdot \frac{1}{2} u^{2}

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2} u^{2}

Eliminar los terminos comunes:

2

= u^{2} \cdot 1

Multiplicar:

u^{2} \cdot 1 = u^{2}

= u^{2}

Simplificar

\frac{1 \cdot 2}{2} : 1

\frac{1 \cdot 2}{2}

Multiplicar los numeros:

1 \cdot 2 = 2

= \frac{2}{2}

Aplicar la regla

\frac{a}{a} = 1

= 1

u^{2} = 1

u^{2} = 1

u^{2} = 1

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

Aplicar la regla

1 = 1

= 1

- 1 = - 1

- 1

Aplicar la regla

1 = 1

= - 1

u = 1, u = - 1

Sustituir en la ecuación

u = cos (x)

cos (x) = 1, cos (x) = - 1

cos (x) = 1, cos (x) = - 1

cos (x) = 1 : x = 2 πn

cos (x) = 1

Soluciones generales para

cos (x) = 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}

x = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

Soluciones generales para

cos (x) = - 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}

x = π + 2 πn

x = π + 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn

Ejemplos populares

3tan(x)= 1/(cos(x))

3 tan (x) = \frac{1}{cos ( x )}

cos(x)-sin(x)=0,-pi<= x<= pi

cos (x) - sin (x) = 0, - π \leq x \leq π

5 - tan^{2} (x) = 4

2sec^2(θ)-3=tan^2(θ)

2 sec^{2} (θ) - 3 = tan^{2} (θ)

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

sin (π - x) + cos (x) = 0