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Popular >

sin(5/2 θ)=-0.966

Solución

sin (\frac{5}{2} θ) = - 0.966

θ = - \frac{2 \cdot 1.30928 \dots}{5} + \frac{4 πn}{5}, θ = \frac{2 π}{5} + \frac{2 \cdot 1.30928 \dots}{5} + \frac{4 πn}{5}

Grados

θ = - 30.00657 \dots^{\circ} + 14 4^{\circ} n, θ = 102.00657 \dots^{\circ} + 14 4^{\circ} n

Pasos de solución

sin (\frac{5}{2} θ) = - 0.966

Aplicar propiedades trigonométricas inversas

sin (\frac{5}{2} θ) = - 0.966

Soluciones generales para

sin (\frac{5}{2} θ) = - 0.966

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

\frac{5}{2} θ = arcsin (- 0.966) + 2 πn, \frac{5}{2} θ = π + arcsin (0.966) + 2 πn

\frac{5}{2} θ = arcsin (- 0.966) + 2 πn, \frac{5}{2} θ = π + arcsin (0.966) + 2 πn

Resolver

\frac{5}{2} θ = arcsin (- 0.966) + 2 πn : θ = - \frac{2 arcsin ( \frac{483}{500} )}{5} + \frac{4 πn}{5}

\frac{5}{2} θ = arcsin (- 0.966) + 2 πn

Simplificar

arcsin (- 0.966) + 2 πn : - arcsin (\frac{483}{500}) + 2 πn

arcsin (- 0.966) + 2 πn

arcsin (- 0.966) = - arcsin (\frac{483}{500})

arcsin (- 0.966)

= arcsin (- \frac{483}{500})

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{483}{500}) = - arcsin (\frac{483}{500})

= - arcsin (\frac{483}{500})

= - arcsin (\frac{483}{500}) + 2 πn

\frac{5}{2} θ = - arcsin (\frac{483}{500}) + 2 πn

Multiplicar ambos lados por

2

\frac{5}{2} θ = - arcsin (\frac{483}{500}) + 2 πn

Multiplicar ambos lados por

2

2 \cdot \frac{5}{2} θ = - 2 arcsin (\frac{483}{500}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{5}{2} θ = - 2 arcsin (\frac{483}{500}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{5}{2} θ : 5 θ

2 \cdot \frac{5}{2} θ

Multiplicar fracciones:

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

= \frac{5 \cdot 2}{2} θ

Eliminar los terminos comunes:

2

= θ \cdot 5

Simplificar

- 2 arcsin (\frac{483}{500}) + 2 \cdot 2 πn : - 2 arcsin (\frac{483}{500}) + 4 πn

- 2 arcsin (\frac{483}{500}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= - 2 arcsin (\frac{483}{500}) + 4 πn

5 θ = - 2 arcsin (\frac{483}{500}) + 4 πn

5 θ = - 2 arcsin (\frac{483}{500}) + 4 πn

5 θ = - 2 arcsin (\frac{483}{500}) + 4 πn

Dividir ambos lados entre

5

5 θ = - 2 arcsin (\frac{483}{500}) + 4 πn

Dividir ambos lados entre

5

\frac{5 θ}{5} = - \frac{2 arcsin ( \frac{483}{500} )}{5} + \frac{4 πn}{5}

Simplificar

θ = - \frac{2 arcsin ( \frac{483}{500} )}{5} + \frac{4 πn}{5}

θ = - \frac{2 arcsin ( \frac{483}{500} )}{5} + \frac{4 πn}{5}

Resolver

\frac{5}{2} θ = π + arcsin (0.966) + 2 πn : θ = \frac{2 π}{5} + \frac{2 arcsin ( 0.966 )}{5} + \frac{4 πn}{5}

\frac{5}{2} θ = π + arcsin (0.966) + 2 πn

Multiplicar ambos lados por

2

\frac{5}{2} θ = π + arcsin (0.966) + 2 πn

Multiplicar ambos lados por

2

2 \cdot \frac{5}{2} θ = 2 π + 2 arcsin (0.966) + 2 \cdot 2 πn

Simplificar

5 θ = 2 π + 2 arcsin (0.966) + 4 πn

5 θ = 2 π + 2 arcsin (0.966) + 4 πn

Dividir ambos lados entre

5

5 θ = 2 π + 2 arcsin (0.966) + 4 πn

Dividir ambos lados entre

5

\frac{5 θ}{5} = \frac{2 π}{5} + \frac{2 arcsin ( 0.966 )}{5} + \frac{4 πn}{5}

Simplificar

θ = \frac{2 π}{5} + \frac{2 arcsin ( 0.966 )}{5} + \frac{4 πn}{5}

θ = \frac{2 π}{5} + \frac{2 arcsin ( 0.966 )}{5} + \frac{4 πn}{5}

θ = - \frac{2 arcsin ( \frac{483}{500} )}{5} + \frac{4 πn}{5}, θ = \frac{2 π}{5} + \frac{2 arcsin ( 0.966 )}{5} + \frac{4 πn}{5}

Mostrar soluciones en forma decimal

θ = - \frac{2 \cdot 1.30928 \dots}{5} + \frac{4 πn}{5}, θ = \frac{2 π}{5} + \frac{2 \cdot 1.30928 \dots}{5} + \frac{4 πn}{5}

sin^{2} (x) - \frac{2}{3} = 0

0 = - 8 sin (x)

cos^{2} (x) + 2 cos (x) + 1 = 0, (0, 2 π)

3 sin (2 θ) = 2 sin (θ)

sin (x) \cdot cos^{2} (x) = sin (x)