sin(2x)-cos(3x)=0

Solución

sin (2 x) - cos (3 x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.31415 \dots + 2 πn, x = π - 0.31415 \dots + 2 πn, x = - 0.94247 \dots + 2 πn, x = π + 0.94247 \dots + 2 πn

Pasos de solución

sin (2 x) - cos (3 x) = 0

Re-escribir usando identidades trigonométricas

3 cos (x) - 4 cos^{3} (x) + 2 cos (x) sin (x) = 0

Factorizar

3 cos (x) - 4 cos^{3} (x) + 2 cos (x) sin (x) : cos (x) (3 - 4 cos^{2} (x) + 2 sin (x))

cos (x) (3 - 4 cos^{2} (x) + 2 sin (x)) = 0

Resolver cada parte por separado

cos (x) = 0 or 3 - 4 cos^{2} (x) + 2 sin (x) = 0

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

3 - 4 cos^{2} (x) + 2 sin (x) = 0 : x = arcsin (\frac{- 1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{4}) + 2 πn, x = arcsin (- \frac{1 + 5}{4}) + 2 πn, x = π + arcsin (\frac{1 + 5}{4}) + 2 πn

Combinar toda las soluciones

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arcsin (\frac{- 1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{4}) + 2 πn, x = arcsin (- \frac{1 + 5}{4}) + 2 πn, x = π + arcsin (\frac{1 + 5}{4}) + 2 πn

Mostrar soluciones en forma decimal

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.31415 \dots + 2 πn, x = π - 0.31415 \dots + 2 πn, x = - 0.94247 \dots + 2 πn, x = π + 0.94247 \dots + 2 πn

tan (θ) = - 4

cos (θ) = - \frac{1}{3}

2 cos (θ) = 2

4 sin (θ) - 1 = 2 sin (θ)

sin (3 θ + \frac{π}{18}) = 1