English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometría >

5sin^2(x)=2sin(x)

Solución

5 sin^{2} (x) = 2 sin (x)

Solución

x = 2 πn, x = π + 2 πn, x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 156.42182 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

5 sin^{2} (x) = 2 sin (x)

Usando el método de sustitución

5 sin^{2} (x) = 2 sin (x)

Sea:

sin (x) = u

5 u^{2} = 2 u

5 u^{2} = 2 u : u = 0, u = \frac{2}{5}

5 u^{2} = 2 u

Desplace

2 u

a la izquierda

5 u^{2} = 2 u

Restar

2 u

de ambos lados

5 u^{2} - 2 u = 2 u - 2 u

Simplificar

5 u^{2} - 2 u = 0

5 u^{2} - 2 u = 0

Factorizar

5 u^{2} - 2 u : u (5 u - 2)

5 u^{2} - 2 u

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 5 uu - 2 u

Factorizar el termino común

u

= u (5 u - 2)

u (5 u - 2) = 0

Usando la propiedad del factor cero:

ab = 0

entonces

a = 0

b = 0

u = 0 or 5 u - 2 = 0

Resolver

5 u - 2 = 0 : u = \frac{2}{5}

5 u - 2 = 0

Desplace

2

a la derecha

5 u - 2 = 0

Sumar

2

a ambos lados

5 u - 2 + 2 = 0 + 2

Simplificar

5 u = 2

5 u = 2

Dividir ambos lados entre

5

5 u = 2

Dividir ambos lados entre

5

\frac{5 u}{5} = \frac{2}{5}

Simplificar

u = \frac{2}{5}

u = \frac{2}{5}

Las soluciones a la ecuación de segundo grado son:

u = 0, u = \frac{2}{5}

Sustituir en la ecuación

u = sin (x)

sin (x) = 0, sin (x) = \frac{2}{5}

sin (x) = 0, sin (x) = \frac{2}{5}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

Soluciones generales para

sin (x) = 0

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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 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, x = π + 2 πn

sin (x) = \frac{2}{5} : x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

sin (x) = \frac{2}{5}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{2}{5}

Soluciones generales para

sin (x) = \frac{2}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn, x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

Mostrar soluciones en forma decimal

x = 2 πn, x = π + 2 πn, x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

Gráfica

Ejemplos populares

3cos^2(x)+5sin(x)-4=0

solvefor x,d^2+3d+2y=4cos^2(x)

(1+tan^2(x))cos^2(x)=sec(x)

(cos^2(x)-1)/(sin^2(x))=-tan(x)

cos^6(x)=-cos^2(x)