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sec((5θ)/4)=2,[0.2pi]

Solución

sec (\frac{5 θ}{4}) = 2, [0.2 π]

Solución

Sin soluci \overset{o}{ˊ} n para θ \in R

Pasos de solución

sec (\frac{5 θ}{4}) = 2, [0.2 π]

Soluciones generales para

sec (\frac{5 θ}{4}) = 2

sec (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

\frac{5 θ}{4} = \frac{π}{3} + 2 πn, \frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

\frac{5 θ}{4} = \frac{π}{3} + 2 πn, \frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

Resolver

\frac{5 θ}{4} = \frac{π}{3} + 2 πn : θ = \frac{4 π}{15} + \frac{8 πn}{5}

\frac{5 θ}{4} = \frac{π}{3} + 2 πn

Multiplicar ambos lados por

4

\frac{5 θ}{4} = \frac{π}{3} + 2 πn

Multiplicar ambos lados por

4

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{π}{3} + 4 \cdot 2 πn

Simplificar

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{π}{3} + 4 \cdot 2 πn

Simplificar

\frac{4 \cdot 5 θ}{4} : 5 θ

\frac{4 \cdot 5 θ}{4}

Multiplicar los numeros:

4 \cdot 5 = 20

= \frac{20 θ}{4}

Dividir:

\frac{20}{4} = 5

= 5 θ

Simplificar

4 \cdot \frac{π}{3} + 4 \cdot 2 πn : \frac{4 π}{3} + 8 πn

4 \cdot \frac{π}{3} + 4 \cdot 2 πn

Multiplicar

4 \cdot \frac{π}{3} : \frac{4 π}{3}

4 \cdot \frac{π}{3}

Multiplicar fracciones:

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

= \frac{π 4}{3}

= \frac{4 π}{3} + 4 \cdot 2 πn

Multiplicar los numeros:

4 \cdot 2 = 8

= \frac{4 π}{3} + 8 πn

5 θ = \frac{4 π}{3} + 8 πn

5 θ = \frac{4 π}{3} + 8 πn

5 θ = \frac{4 π}{3} + 8 πn

Dividir ambos lados entre

5

5 θ = \frac{4 π}{3} + 8 πn

Dividir ambos lados entre

5

\frac{5 θ}{5} = \frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5}

Simplificar

\frac{5 θ}{5} = \frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5}

Simplificar

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Dividir:

\frac{5}{5} = 1

= θ

Simplificar

\frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5} : \frac{4 π}{15} + \frac{8 πn}{5}

\frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5}

\frac{\frac{4 π}{3}}{5} = \frac{4 π}{15}

\frac{\frac{4 π}{3}}{5}

Aplicar las propiedades de las fracciones:

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

= \frac{4 π}{3 \cdot 5}

Multiplicar los numeros:

3 \cdot 5 = 15

= \frac{4 π}{15}

= \frac{4 π}{15} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}

Resolver

\frac{5 θ}{4} = \frac{5 π}{3} + 2 πn : θ = \frac{4 π}{3} + \frac{8 πn}{5}

\frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

Multiplicar ambos lados por

4

\frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

Multiplicar ambos lados por

4

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

Simplificar

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

Simplificar

\frac{4 \cdot 5 θ}{4} : 5 θ

\frac{4 \cdot 5 θ}{4}

Multiplicar los numeros:

4 \cdot 5 = 20

= \frac{20 θ}{4}

Dividir:

\frac{20}{4} = 5

= 5 θ

Simplificar

4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn : \frac{20 π}{3} + 8 πn

4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

4 \cdot \frac{5 π}{3} = \frac{20 π}{3}

4 \cdot \frac{5 π}{3}

Multiplicar fracciones:

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

= \frac{5 π 4}{3}

Multiplicar los numeros:

5 \cdot 4 = 20

= \frac{20 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiplicar los numeros:

4 \cdot 2 = 8

= 8 πn

= \frac{20 π}{3} + 8 πn

5 θ = \frac{20 π}{3} + 8 πn

5 θ = \frac{20 π}{3} + 8 πn

5 θ = \frac{20 π}{3} + 8 πn

Dividir ambos lados entre

5

5 θ = \frac{20 π}{3} + 8 πn

Dividir ambos lados entre

5

\frac{5 θ}{5} = \frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5}

Simplificar

\frac{5 θ}{5} = \frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5}

Simplificar

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Dividir:

\frac{5}{5} = 1

= θ

Simplificar

\frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5} : \frac{4 π}{3} + \frac{8 πn}{5}

\frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5}

\frac{\frac{20 π}{3}}{5} = \frac{4 π}{3}

\frac{\frac{20 π}{3}}{5}

Aplicar las propiedades de las fracciones:

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

= \frac{20 π}{3 \cdot 5}

Multiplicar los numeros:

3 \cdot 5 = 15

= \frac{20 π}{15}

Eliminar los terminos comunes:

5

= \frac{4 π}{3}

= \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}, θ = \frac{4 π}{3} + \frac{8 πn}{5}

Soluciones para el rango

[0.2 π]

Sin soluci \overset{o}{ˊ} n para θ \in R

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