9/2 cos^2(x)-2=0

Solución

\frac{9}{2} cos^{2} (x) - 2 = 0

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn, x = 2.30052 \dots + 2 πn, x = - 2.30052 \dots + 2 πn

Pasos de solución

\frac{9}{2} cos^{2} (x) - 2 = 0

Usando el método de sustitución

cos (x) = \frac{2}{3}, cos (x) = - \frac{2}{3}

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

cos (x) = - \frac{2}{3} : x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

Combinar toda las soluciones

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn, x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn, x = 2.30052 \dots + 2 πn, x = - 2.30052 \dots + 2 πn

\frac{1}{2} = cos (3 x)

3 cos (θ) = 2 + 2 sin (θ)

1.65 \cdot sin (3 0^{\circ}) = 1.33 \cdot sin (x)

sin (x) + cos (x) = \frac{3}{2}

cos (2 x) - sin (x) = 0.5