sin((4pi)/(11))=sin(θ)*sin((7pi)/(11))

Solución

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

θ = 1.57079 \dots + 2 πn

Grados

θ = 89.99999 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

sin (\frac{4 π}{11}) = sin (θ) sin (\frac{7 π}{11})

Intercambiar lados

sin (θ) sin (\frac{7 π}{11}) = sin (\frac{4 π}{11})

Dividir ambos lados entre

sin (\frac{7 π}{11})

sin (θ) sin (\frac{7 π}{11}) = sin (\frac{4 π}{11})

Dividir ambos lados entre

sin (\frac{7 π}{11})

\frac{sin ( θ ) sin ( \frac{7 π}{11} )}{sin ( \frac{7 π}{11} )} = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

Simplificar

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

Aplicar propiedades trigonométricas inversas

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

Soluciones generales para

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn, θ = π - arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn, θ = π - arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

Mezclar intervalos sobrepuestos

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

Mostrar soluciones en forma decimal

θ = 1.57079 \dots + 2 πn

sin (2 x) = 2 tan (2 x)

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

sec^{2} (x) + sec (x) - 2 = 0

(cot (x) - 1) (2 sin (x) + 1) = 0

y, x = tan (y)