English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)cos(x)-2cos^2(x)=0,0<x<360

Solución

3 cos (x) - 2 cos^{2} (x) = 0, 0^{\circ} < x < 36 0^{\circ}

Solución

x = 9 0^{\circ}, x = 27 0^{\circ}, x = 3 0^{\circ}, x = 33 0^{\circ}

radianes

x = \frac{π}{2}, x = \frac{3 π}{2}, x = \frac{π}{6}, x = \frac{11 π}{6}

Pasos de solución

3 cos (x) - 2 cos^{2} (x) = 0, 0^{\circ} < x < 36 0^{\circ}

Usando el método de sustitución

3 cos (x) - 2 cos^{2} (x) = 0

Sea:

cos (x) = u

3 u - 2 u^{2} = 0

3 u - 2 u^{2} = 0 : u = 0, u = \frac{3}{2}

3 u - 2 u^{2} = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

- 2 u^{2} + 3 u = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

- 2 u^{2} + 3 u = 0

Formula general para ecuaciones de segundo grado:

Para

a = - 2, b = 3, c = 0

u_{1, 2} = \frac{- 3 \pm ( 3 ) ^{2} - 4 ( - 2 ) \cdot 0}{2 ( - 2 )}

u_{1, 2} = \frac{- 3 \pm ( 3 ) ^{2} - 4 ( - 2 ) \cdot 0}{2 ( - 2 )}

(3)^{2} - 4 (- 2) \cdot 0 = 3

(3)^{2} - 4 (- 2) \cdot 0

Aplicar la regla

- (- a) = a

= (3)^{2} + 4 \cdot 2 \cdot 0

(3)^{2} = 3

(3)^{2}

Aplicar las leyes de los exponentes:

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

= (3^{\frac{1}{2}})^{2}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

2

= 1

= 3

4 \cdot 2 \cdot 0 = 0

4 \cdot 2 \cdot 0

Aplicar la regla

0 \cdot a = 0

= 0

= 3 + 0

Sumar:

3 + 0 = 3

= 3

u_{1, 2} = \frac{- 3 \pm 3}{2 ( - 2 )}

Separar las soluciones

u_{1} = \frac{- 3 + 3}{2 ( - 2 )}, u_{2} = \frac{- 3 - 3}{2 ( - 2 )}

u = \frac{- 3 + 3}{2 ( - 2 )} : 0

\frac{- 3 + 3}{2 ( - 2 )}

Quitar los parentesis:

(- a) = - a

= \frac{- 3 + 3}{- 2 \cdot 2}

Sumar elementos similares:

- 3 + 3 = 0

= \frac{0}{- 2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{0}{- 4}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{0}{4}

Aplicar la regla

\frac{0}{a} = 0, a \neq = 0

= - 0

= 0

u = \frac{- 3 - 3}{2 ( - 2 )} : \frac{3}{2}

\frac{- 3 - 3}{2 ( - 2 )}

Quitar los parentesis:

(- a) = - a

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

Sumar elementos similares:

- 3 - 3 = - 23

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

Multiplicar los numeros:

2 \cdot 2 = 4

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

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 3}{4}

Eliminar los terminos comunes:

2

= \frac{3}{2}

Las soluciones a la ecuación de segundo grado son:

u = 0, u = \frac{3}{2}

Sustituir en la ecuación

u = cos (x)

cos (x) = 0, cos (x) = \frac{3}{2}

cos (x) = 0, cos (x) = \frac{3}{2}

cos (x) = 0, 0 < x < 36 0^{\circ} : x = 9 0^{\circ}, x = 27 0^{\circ}

cos (x) = 0, 0 < x < 36 0^{\circ}

Soluciones generales para

cos (x) = 0

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Soluciones para el rango

0 < x < 36 0^{\circ}

x = 9 0^{\circ}, x = 27 0^{\circ}

cos (x) = \frac{3}{2}, 0 < x < 36 0^{\circ} : x = 3 0^{\circ}, x = 33 0^{\circ}

cos (x) = \frac{3}{2}, 0 < x < 36 0^{\circ}

Soluciones generales para

cos (x) = \frac{3}{2}

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Soluciones para el rango

0 < x < 36 0^{\circ}

x = 3 0^{\circ}, x = 33 0^{\circ}

Combinar toda las soluciones

x = 9 0^{\circ}, x = 27 0^{\circ}, x = 3 0^{\circ}, x = 33 0^{\circ}

Ejemplos populares

sin^2(x)cos(x)-sin(x)cos^3(x)=0

sin^{2} (x) cos (x) - sin (x) cos^{3} (x) = 0

5sin(θ)-sqrt(3)=3sin(θ)

5 sin (θ) - 3 = 3 sin (θ)

sin^3(x)-4sin(x)=0

sin^{3} (x) - 4 sin (x) = 0

cos(a)=(-82)/(sqrt(140)*\sqrt{138)}

cos (a) = \frac{- 82}{140 \cdot 138}

sec^2(x)-cos(x)=0

sec^{2} (x) - cos (x) = 0