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Popular Trigonometría >

sec(θ/5)=sqrt(7)

Solución

sec (\frac{θ}{5}) = 7

Solución

θ = 5 \cdot 1.18319 \dots + 10 πn, θ = 10 π - 5 \cdot 1.18319 \dots + 10 πn

+1

Grados

θ = 338.96172 \dots^{\circ} + 180 0^{\circ} n, θ = 1461.03827 \dots^{\circ} + 180 0^{\circ} n

Pasos de solución

sec (\frac{θ}{5}) = 7

Aplicar propiedades trigonométricas inversas

sec (\frac{θ}{5}) = 7

Soluciones generales para

sec (\frac{θ}{5}) = 7

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

\frac{θ}{5} = arcsec (7) + 2 πn, \frac{θ}{5} = 2 π - arcsec (7) + 2 πn

\frac{θ}{5} = arcsec (7) + 2 πn, \frac{θ}{5} = 2 π - arcsec (7) + 2 πn

Resolver

\frac{θ}{5} = arcsec (7) + 2 πn : θ = 5 arcsec (7) + 10 πn

\frac{θ}{5} = arcsec (7) + 2 πn

Multiplicar ambos lados por

5

\frac{θ}{5} = arcsec (7) + 2 πn

Multiplicar ambos lados por

5

\frac{5 θ}{5} = 5 arcsec (7) + 5 \cdot 2 πn

Simplificar

\frac{5 θ}{5} = 5 arcsec (7) + 5 \cdot 2 πn

Simplificar

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Dividir:

\frac{5}{5} = 1

= θ

Simplificar

5 arcsec (7) + 5 \cdot 2 πn : 5 arcsec (7) + 10 πn

5 arcsec (7) + 5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

Resolver

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn : θ = 10 π - 5 arcsec (7) + 10 πn

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn

Multiplicar ambos lados por

5

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn

Multiplicar ambos lados por

5

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

Simplificar

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

Simplificar

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Dividir:

\frac{5}{5} = 1

= θ

Simplificar

5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn : 10 π - 5 arcsec (7) + 10 πn

5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn, θ = 10 π - 5 arcsec (7) + 10 πn

Mostrar soluciones en forma decimal

θ = 5 \cdot 1.18319 \dots + 10 πn, θ = 10 π - 5 \cdot 1.18319 \dots + 10 πn

Gráfica

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