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Popular >

sin^2(x)=2sin(x)cos(x)

Solución

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

Solución

x = 2 πn, x = π + 2 πn, x = 1.10714 \dots + πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Restar

2 sin (x) cos (x)

de ambos lados

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

Factorizar

sin^{2} (x) - 2 sin (x) cos (x) : sin (x) (sin (x) - 2 cos (x))

sin^{2} (x) - 2 sin (x) cos (x)

Aplicar las leyes de los exponentes:

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

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

= sin (x) sin (x) - 2 sin (x) cos (x)

Factorizar el termino común

sin (x)

= sin (x) (sin (x) - 2 cos (x))

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

Resolver cada parte por separado

sin (x) = 0 or sin (x) - 2 cos (x) = 0

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) - 2 cos (x) = 0 : x = arctan (2) + πn

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

cos (x), cos (x) \neq = 0

\frac{sin ( x ) - 2 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplificar

\frac{sin ( x )}{cos ( x )} - 2 = 0

Utilizar la identidad trigonométrica básica:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (x) - 2 = 0

tan (x) - 2 = 0

Mover

2

al lado derecho

tan (x) - 2 = 0

Sumar

2

a ambos lados

tan (x) - 2 + 2 = 0 + 2

Simplificar

tan (x) = 2

tan (x) = 2

Aplicar propiedades trigonométricas inversas

tan (x) = 2

Soluciones generales para

tan (x) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (2) + πn

x = arctan (2) + πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn, x = arctan (2) + πn

Mostrar soluciones en forma decimal

x = 2 πn, x = π + 2 πn, x = 1.10714 \dots + πn

Ejemplos populares

cos (x) = 0.77

cos(θ)=-3/(sqrt(5))

cos (θ) = - \frac{3}{5}

2sec(x)+tan^2(x)-9=1

2 sec (x) + tan^{2} (x) - 9 = 1

sin (x) = 1.34

tan(x)sin^2(x)=sin(2x)

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