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Popular >

sin(x+pi/4)=\pm 1

Solución

sin (x + \frac{π}{4}) = \pm 1

Solución

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

sin (x + \frac{π}{4}) = \pm 1

Aplicar propiedades trigonométricas inversas

sin (x + \frac{π}{4}) = \pm 1

Soluciones generales para

sin (x + \frac{π}{4}) = \pm 1

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

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

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

Resolver

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn : x = arcsin (\pm 1) + 2 πn - \frac{π}{4}

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn

Mover

\frac{π}{4}

al lado derecho

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn

Restar

\frac{π}{4}

de ambos lados

x + \frac{π}{4} - \frac{π}{4} = arcsin (\pm 1) + 2 πn - \frac{π}{4}

Simplificar

x = arcsin (\pm 1) + 2 πn - \frac{π}{4}

x = arcsin (\pm 1) + 2 πn - \frac{π}{4}

Resolver

x + \frac{π}{4} = π + arcsin (- \pm 1) + 2 πn : x = π + arcsin (- \pm 1) + 2 πn - \frac{π}{4}

x + \frac{π}{4} = π + arcsin (- \pm 1) + 2 πn

Mover

\frac{π}{4}

al lado derecho

x + \frac{π}{4} = π + arcsin (- \pm 1) + 2 πn

Restar

\frac{π}{4}

de ambos lados

x + \frac{π}{4} - \frac{π}{4} = π + arcsin (- \pm 1) + 2 πn - \frac{π}{4}

Simplificar

x = π + arcsin (- \pm 1) + 2 πn - \frac{π}{4}

x = π + arcsin (- \pm 1) + 2 πn - \frac{π}{4}

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

Siendo que la ecuación esta indefinida para:

arcsin (\pm 1) + 2 πn - \frac{π}{4}, π + arcsin (- \pm 1) + 2 πn - \frac{π}{4}

Sin soluci \overset{o}{ˊ} n para x \in R

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