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Popular Trigonometría >

(sin(2θ))/2 <= 0.451

Solución

\frac{sin ( 2 θ )}{2} \leq 0.451

Solución

\frac{- π - 1.12437 \dots}{2} + πn \leq θ \leq 0.56218 \dots + πn

+2

Notación de intervalos

[\frac{- π - 1.12437 \dots}{2} + πn, 0.56218 \dots + πn]

Decimal

- 2.13298 \dots + πn \leq θ \leq 0.56218 \dots + πn

Pasos de solución

\frac{sin ( 2 θ )}{2} \leq 0.451

Multiplicar ambos lados por

2

\frac{sin ( 2 θ )}{2} \leq 0.451

Multiplicar ambos lados por

2

\frac{2 sin ( 2 θ )}{2} \leq 0.451 \cdot 2

Simplificar

sin (2 θ) \leq 0.902

sin (2 θ) \leq 0.902

Para

sin (x) \leq a

, si

- 1 < a < 1

entonces

- π - arcsin (a) + 2 πn \leq x \leq arcsin (a) + 2 πn

- π - arcsin (0.902) + 2 πn \leq 2 θ \leq arcsin (0.902) + 2 πn

Pi

a \leq u \leq b

entonces

a \leq u and u \leq b

- π - arcsin (0.902) + 2 πn \leq 2 θ and 2 θ \leq arcsin (0.902) + 2 πn

- π - arcsin (0.902) + 2 πn \leq 2 θ : θ \geq \frac{- π - arcsin ( 0.902 )}{2} + πn

- π - arcsin (0.902) + 2 πn \leq 2 θ

Intercambiar lados

2 θ \geq - π - arcsin (0.902) + 2 πn

Dividir ambos lados entre

2

2 θ \geq - π - arcsin (0.902) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} \geq - \frac{π}{2} - \frac{arcsin ( 0.902 )}{2} + \frac{2 πn}{2}

Simplificar

θ \geq - \frac{π}{2} - \frac{arcsin ( 0.902 )}{2} + πn

Simplificar

- \frac{π}{2} - \frac{arcsin ( 0.902 )}{2} : \frac{- π - arcsin ( 0.902 )}{2}

- \frac{π}{2} - \frac{arcsin ( 0.902 )}{2}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- π - arcsin ( 0.902 )}{2}

θ \geq \frac{- π - arcsin ( 0.902 )}{2} + πn

θ \geq \frac{- π - arcsin ( 0.902 )}{2} + πn

2 θ \leq arcsin (0.902) + 2 πn : θ \leq \frac{arcsin ( 0.902 )}{2} + πn

2 θ \leq arcsin (0.902) + 2 πn

Dividir ambos lados entre

2

2 θ \leq arcsin (0.902) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} \leq \frac{arcsin ( 0.902 )}{2} + \frac{2 πn}{2}

Simplificar

θ \leq \frac{arcsin ( 0.902 )}{2} + πn

θ \leq \frac{arcsin ( 0.902 )}{2} + πn

Combinar los rangos

θ \geq \frac{- π - arcsin ( 0.902 )}{2} + πn and θ \leq \frac{arcsin ( 0.902 )}{2} + πn

Mezclar intervalos sobrepuestos

\frac{- π - 1.12437 \dots}{2} + πn \leq θ \leq 0.56218 \dots + πn

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