sin(x)=sin(x^2)

Solución

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

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

Pasos de solución

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

Restar

sin (x^{2})

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Resolver cada parte por separado

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

cos (\frac{x + x ^{2}}{2}) = 0 : x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

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

Sin solución

Combinar toda las soluciones

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

sin (x) = - 0.23

2 sin^{2} (x) + 3 sin (x) + 1 = 0, 0 \leq x \leq 2 π

cos (3 x) - 1 = sin (3 x)

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

2 cos (3 x) = - 3