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Popular >

sin(x/3)=-0.85

Solución

sin (\frac{x}{3}) = - 0.85

Solución

x = - 3 \cdot 1.01598 \dots + 6 πn, x = 3 π + 3 \cdot 1.01598 \dots + 6 πn

+1

Grados

x = - 174.63500 \dots^{\circ} + 108 0^{\circ} n, x = 714.63500 \dots^{\circ} + 108 0^{\circ} n

Pasos de solución

sin (\frac{x}{3}) = - 0.85

Aplicar propiedades trigonométricas inversas

sin (\frac{x}{3}) = - 0.85

Soluciones generales para

sin (\frac{x}{3}) = - 0.85

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

\frac{x}{3} = arcsin (- 0.85) + 2 πn, \frac{x}{3} = π + arcsin (0.85) + 2 πn

\frac{x}{3} = arcsin (- 0.85) + 2 πn, \frac{x}{3} = π + arcsin (0.85) + 2 πn

Resolver

\frac{x}{3} = arcsin (- 0.85) + 2 πn : x = - 3 arcsin (\frac{17}{20}) + 6 πn

\frac{x}{3} = arcsin (- 0.85) + 2 πn

Simplificar

arcsin (- 0.85) + 2 πn : - arcsin (\frac{17}{20}) + 2 πn

arcsin (- 0.85) + 2 πn

arcsin (- 0.85) = - arcsin (\frac{17}{20})

arcsin (- 0.85)

= arcsin (- \frac{17}{20})

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{17}{20}) = - arcsin (\frac{17}{20})

= - arcsin (\frac{17}{20})

= - arcsin (\frac{17}{20}) + 2 πn

\frac{x}{3} = - arcsin (\frac{17}{20}) + 2 πn

Multiplicar ambos lados por

3

\frac{x}{3} = - arcsin (\frac{17}{20}) + 2 πn

Multiplicar ambos lados por

3

\frac{3 x}{3} = - 3 arcsin (\frac{17}{20}) + 3 \cdot 2 πn

Simplificar

\frac{3 x}{3} = - 3 arcsin (\frac{17}{20}) + 3 \cdot 2 πn

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

- 3 arcsin (\frac{17}{20}) + 3 \cdot 2 πn : - 3 arcsin (\frac{17}{20}) + 6 πn

- 3 arcsin (\frac{17}{20}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= - 3 arcsin (\frac{17}{20}) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 πn

Resolver

\frac{x}{3} = π + arcsin (0.85) + 2 πn : x = 3 π + 3 arcsin (0.85) + 6 πn

\frac{x}{3} = π + arcsin (0.85) + 2 πn

Multiplicar ambos lados por

3

\frac{x}{3} = π + arcsin (0.85) + 2 πn

Multiplicar ambos lados por

3

\frac{3 x}{3} = 3 π + 3 arcsin (0.85) + 3 \cdot 2 πn

Simplificar

x = 3 π + 3 arcsin (0.85) + 6 πn

x = 3 π + 3 arcsin (0.85) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 πn, x = 3 π + 3 arcsin (0.85) + 6 πn

Mostrar soluciones en forma decimal

x = - 3 \cdot 1.01598 \dots + 6 πn, x = 3 π + 3 \cdot 1.01598 \dots + 6 πn

Ejemplos populares

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tan(θ)=2,0<θ<(pi/2),sin(θ/2)

tan (θ) = 2, 0 < θ < (\frac{π}{2}), sin (\frac{θ}{2})

sinh (a) = \frac{1}{2}

sin(x)=(-1}{\frac{sqrt(5))/2}

sin (x) = \frac{- 1}{\frac{5}{2}}

2csc^2(θ)-3cot(θ)+3=0

2 csc^{2} (θ) - 3 cot (θ) + 3 = 0