sin(x)-cos(x)=-1,0<= x<= 2pi

Solución

sin (x) - cos (x) = - 1, 0 \leq x \leq 2 π

x = \frac{3 π}{2}, x = 2 π, x = 0

Pasos de solución

sin (x) - cos (x) = - 1, 0 \leq x \leq 2 π

Re-escribir usando identidades trigonométricas

2 sin (x - \frac{π}{4}) = - 1

Dividir ambos lados entre

2

sin (x - \frac{π}{4}) = - \frac{2}{2}

Soluciones generales para

sin (x - \frac{π}{4}) = - \frac{2}{2}

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn, x - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Resolver

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

Resolver

x - \frac{π}{4} = \frac{7 π}{4} + 2 πn : x = 2 πn + 2 π

x = 2 πn + \frac{3 π}{2}, x = 2 πn + 2 π

Soluciones para el rango

0 \leq x \leq 2 π

x = \frac{3 π}{2}, x = 2 π, x = 0

cos (θ) = (\frac{1}{2})

sin^{2} (x) - cos^{2} (x) + sin (x) = 0, 0 \leq x \leq 2 π

cos (θ) = - cos (2 θ)

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

\frac{sin ( 2 x )}{sin ( x )} = 1