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Popular >

sin^3(x)=sin^2(x)

Solución

sin^{3} (x) = sin^{2} (x)

Solución

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

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 9 0^{\circ} + 36 0^{\circ} n

Pasos de solución

sin^{3} (x) = sin^{2} (x)

Usando el método de sustitución

sin^{3} (x) = sin^{2} (x)

Sea:

sin (x) = u

u^{3} = u^{2}

u^{3} = u^{2} : u = 0, u = 1

u^{3} = u^{2}

Mover

u^{2}

al lado izquierdo

u^{3} = u^{2}

Restar

u^{2}

de ambos lados

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

Simplificar

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

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

Factorizar

u^{3} - u^{2} : u^{2} (u - 1)

u^{3} - u^{2}

Aplicar las leyes de los exponentes:

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

u^{3} = u u^{2}

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

Factorizar el termino común

u^{2}

= u^{2} (u - 1)

u^{2} (u - 1) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

u = 0 or u - 1 = 0

Resolver

u - 1 = 0 : u = 1

u - 1 = 0

Mover

1

al lado derecho

u - 1 = 0

Sumar

1

a ambos lados

u - 1 + 1 = 0 + 1

Simplificar

u = 1

u = 1

Las soluciones son

u = 0, u = 1

Sustituir en la ecuación

u = sin (x)

sin (x) = 0, sin (x) = 1

sin (x) = 0, sin (x) = 1

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) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 1

Soluciones generales para

sin (x) = 1

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 = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

Combinar toda las soluciones

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

Ejemplos populares

2sec^2(a)+tan^2(a)=3

2 sec^{2} (a) + tan^{2} (a) = 3

3cos^2(x)+4cos(x)+1=0

3 cos^{2} (x) + 4 cos (x) + 1 = 0

cos^{5} (x) = \frac{1}{2}

(cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

5sec(x)-4cos(x)=8

5 sec (x) - 4 cos (x) = 8