English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(4x)= 1/2 ,0<= x<= 2pi

Solución

cos (4 x) = \frac{1}{2}, 0 \leq x \leq 2 π

x = \frac{π}{12}, x = \frac{5 π}{12}, x = \frac{7 π}{12}, x = \frac{11 π}{12}, x = \frac{13 π}{12}, x = \frac{17 π}{12}, x = \frac{19 π}{12}, x = \frac{23 π}{12}

Grados

x = 1 5^{\circ}, x = 7 5^{\circ}, x = 10 5^{\circ}, x = 16 5^{\circ}, x = 19 5^{\circ}, x = 25 5^{\circ}, x = 28 5^{\circ}, x = 34 5^{\circ}

Pasos de solución

cos (4 x) = \frac{1}{2}, 0 \leq x \leq 2 π

Soluciones generales para

cos (4 x) = \frac{1}{2}

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}

4 x = \frac{π}{3} + 2 πn, 4 x = \frac{5 π}{3} + 2 πn

4 x = \frac{π}{3} + 2 πn, 4 x = \frac{5 π}{3} + 2 πn

Resolver

4 x = \frac{π}{3} + 2 πn : x = \frac{π}{12} + \frac{πn}{2}

4 x = \frac{π}{3} + 2 πn

Dividir ambos lados entre

4

4 x = \frac{π}{3} + 2 πn

Dividir ambos lados entre

4

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

Simplificar

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

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{π}{3}}{4} + \frac{2 πn}{4} : \frac{π}{12} + \frac{πn}{2}

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

\frac{\frac{π}{3}}{4} = \frac{π}{12}

\frac{\frac{π}{3}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{3 \cdot 4}

Multiplicar los numeros:

3 \cdot 4 = 12

= \frac{π}{12}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

Resolver

4 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{12} + \frac{πn}{2}

4 x = \frac{5 π}{3} + 2 πn

Dividir ambos lados entre

4

4 x = \frac{5 π}{3} + 2 πn

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} = \frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4} : \frac{5 π}{12} + \frac{πn}{2}

\frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4}

\frac{\frac{5 π}{3}}{4} = \frac{5 π}{12}

\frac{\frac{5 π}{3}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{5 π}{3 \cdot 4}

Multiplicar los numeros:

3 \cdot 4 = 12

= \frac{5 π}{12}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

Soluciones para el rango

0 \leq x \leq 2 π

x = \frac{π}{12}, x = \frac{5 π}{12}, x = \frac{7 π}{12}, x = \frac{11 π}{12}, x = \frac{13 π}{12}, x = \frac{17 π}{12}, x = \frac{19 π}{12}, x = \frac{23 π}{12}

2 cos^{2} (t) + 3 cos (t) - 5 = 0

6 cos^{2} (x) + 7 sin (x) - 8 = 0

3 csc (x) = 2

4 csc^{2} (x) - 25 = 0

sin (θ) = - \frac{4}{5}, \frac{3 π}{2} < θ < 2 π