cos(x)-sin(x)=0.5

Solución

cos (x) - sin (x) = 0.5

x = \frac{π}{4} + 2 πn - 0.36136 \dots, x = \frac{5 π}{4} + 2 πn + 0.36136 \dots

Pasos de solución

cos (x) - sin (x) = 0.5

Restar

0.5

de ambos lados

cos (x) - sin (x) - 0.5 = 0

Re-escribir usando identidades trigonométricas

- 0.5 - 1.41421 \dots sin (\frac{4 x - π}{4}) = 0

Mover

0.5

al lado derecho

- 1.41421 \dots sin (\frac{4 x - π}{4}) = 0.5

Dividir ambos lados entre

- 1.41421 \dots

sin (\frac{4 x - π}{4}) = - 0.35355 \dots

Aplicar propiedades trigonométricas inversas

\frac{4 x - π}{4} = arcsin (- 0.35355 \dots) + 2 πn, \frac{4 x - π}{4} = π + arcsin (0.35355 \dots) + 2 πn

Resolver

\frac{4 x - π}{4} = arcsin (- 0.35355 \dots) + 2 πn : x = \frac{π}{4} + 2 πn - arcsin (0.35355 \dots)

Resolver

\frac{4 x - π}{4} = π + arcsin (0.35355 \dots) + 2 πn : x = \frac{5 π}{4} + 2 πn + arcsin (0.35355 \dots)

x = \frac{π}{4} + 2 πn - arcsin (0.35355 \dots), x = \frac{5 π}{4} + 2 πn + arcsin (0.35355 \dots)

Mostrar soluciones en forma decimal

x = \frac{π}{4} + 2 πn - 0.36136 \dots, x = \frac{5 π}{4} + 2 πn + 0.36136 \dots

sin (x + π) - sin (x) + 3 = 0

csc (x) = 1.5

tan (t) = 0

cos (\frac{θ}{2}) = \frac{1}{2}

\frac{2}{3} cos (3 θ) = 1