170=(160^2)/(32)sin(2θ)

Solución

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

θ = \frac{0.21413 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.21413 \dots}{2} + πn

Pasos de solución

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

Intercambiar lados

\frac{16 0 ^{2}}{32} sin (2 θ) = 170

Simplificar

\frac{16 0 ^{2}}{32} : 800

800 sin (2 θ) = 170

Dividir ambos lados entre

800

sin (2 θ) = \frac{17}{80}

Aplicar propiedades trigonométricas inversas

2 θ = arcsin (\frac{17}{80}) + 2 πn, 2 θ = π - arcsin (\frac{17}{80}) + 2 πn

Resolver

2 θ = arcsin (\frac{17}{80}) + 2 πn : θ = \frac{arcsin ( \frac{17}{80} )}{2} + πn

Resolver

2 θ = π - arcsin (\frac{17}{80}) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( \frac{17}{80} )}{2} + πn

θ = \frac{arcsin ( \frac{17}{80} )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( \frac{17}{80} )}{2} + πn

Mostrar soluciones en forma decimal

θ = \frac{0.21413 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.21413 \dots}{2} + πn

sin (3 x) = 3 sin (x) cos (x)

sin (x) = \frac{2 π}{5}

sin (x) = \frac{2 π}{7}

cos (θ) sin (θ) = 0

6 cos (6 x - \frac{π}{6}) + 3 = 0