sin(α)+cos(α)= 1/2

Solución

sin (α) + cos (α) = \frac{1}{2}

α = 0.36136 \dots + 2 πn - \frac{π}{4}, α = π - 0.36136 \dots + 2 πn - \frac{π}{4}

Pasos de solución

sin (α) + cos (α) = \frac{1}{2}

Re-escribir usando identidades trigonométricas

2 sin (α + \frac{π}{4}) = \frac{1}{2}

Dividir ambos lados entre

2

sin (α + \frac{π}{4}) = \frac{2}{4}

Aplicar propiedades trigonométricas inversas

α + \frac{π}{4} = arcsin (\frac{2}{4}) + 2 πn, α + \frac{π}{4} = π - arcsin (\frac{2}{4}) + 2 πn

Resolver

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

Resolver

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

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

Mostrar soluciones en forma decimal

α = 0.36136 \dots + 2 πn - \frac{π}{4}, α = π - 0.36136 \dots + 2 πn - \frac{π}{4}

2 sin^{2} (θ) - cos (2 θ) = 1

cos (x - \frac{π}{3}) = - 1

5 tan (B) - 11 = 0

2 csc (x) = 2

2 sin^{2} (x) + 2 cos (x) - 1 = 0