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Popular >

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

Solución

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

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

Restar

sin^{2} (x)

de ambos lados

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

Factorizar

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

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

Aplicar las leyes de los exponentes:

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

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

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

Factorizar el termino común

sin (x)

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

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

Resolver cada parte por separado

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

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

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

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

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

2 - tan (x) = 0

2 - tan (x) = 0

Mover

2

al lado derecho

2 - tan (x) = 0

Restar

2

de ambos lados

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

Simplificar

- tan (x) = - 2

- tan (x) = - 2

Dividir ambos lados entre

- 1

- tan (x) = - 2

Dividir ambos lados entre

- 1

\frac{- tan ( x )}{- 1} = \frac{- 2}{- 1}

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

sin(θ)-0.1cos(θ)=(8.87)/(9.8)

sin (θ) - 0.1 cos (θ) = \frac{8.87}{9.8}

2sin(x)=(sin(x))/(cos(x))

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

6sin^2(x)=5+cos(x),180<= x<= 540

6 sin^{2} (x) = 5 + cos (x), 18 0^{\circ} \leq x \leq 54 0^{\circ}

(cos(x))/2 =(sqrt(3))/2

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

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

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