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Popular >

(sin(2x))/(sin(x))=1.5

Solución

\frac{sin ( 2 x )}{sin ( x )} = 1.5

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Grados

x = 41.40962 \dots^{\circ} + 36 0^{\circ} n, x = 318.59037 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{sin ( 2 x )}{sin ( x )} = 1.5

Restar

1.5

de ambos lados

\frac{sin ( 2 x )}{sin ( x )} - 1.5 = 0

Re-escribir usando identidades trigonométricas

- 1.5 + \frac{sin ( 2 x )}{sin ( x )}

Utilizar la identidad trigonométrica del ángulo doble:

sin (2 x) = 2 sin (x) cos (x)

= - 1.5 + \frac{2 sin ( x ) cos ( x )}{sin ( x )}

Eliminar los terminos comunes:

sin (x)

= - 1.5 + 2 cos (x)

- 1.5 + 2 cos (x) = 0

Mover

1.5

al lado derecho

- 1.5 + 2 cos (x) = 0

Sumar

1.5

a ambos lados

- 1.5 + 2 cos (x) + 1.5 = 0 + 1.5

Simplificar

2 cos (x) = 1.5

2 cos (x) = 1.5

Dividir ambos lados entre

2

2 cos (x) = 1.5

Dividir ambos lados entre

2

\frac{2 cos ( x )}{2} = \frac{1.5}{2}

Simplificar

cos (x) = 0.75

cos (x) = 0.75

Aplicar propiedades trigonométricas inversas

cos (x) = 0.75

Soluciones generales para

cos (x) = 0.75

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

Mostrar soluciones en forma decimal

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

x, yz = sin (x y)

sin^{2} (x) = \frac{( 5 m - 5 )}{2}

2 cot (2 x) = 4

cos (θ) = \frac{4}{3.3 8 ^{2} + 2 ^{2}}

23 sin (2 θ) = 3