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Popular >

solvefor k,1.5=6(-cos(k/2)+1)

Solución

resolver para

k, 1.5 = 6 (- cos (\frac{k}{2}) + 1)

Solución

k = 2 \cdot 0.72273 \dots + 4 πn, k = 4 π - 2 \cdot 0.72273 \dots + 4 πn

+1

Grados

k = 82.81924 \dots^{\circ} + 72 0^{\circ} n, k = 637.18075 \dots^{\circ} + 72 0^{\circ} n

Pasos de solución

1.5 = 6 (- cos (\frac{k}{2}) + 1)

Intercambiar lados

6 (- cos (\frac{k}{2}) + 1) = 1.5

Dividir ambos lados entre

6

6 (- cos (\frac{k}{2}) + 1) = 1.5

Dividir ambos lados entre

6

\frac{6 ( - cos ( \frac{k}{2} ) + 1 )}{6} = \frac{1.5}{6}

Simplificar

- cos (\frac{k}{2}) + 1 = 0.25

- cos (\frac{k}{2}) + 1 = 0.25

Mover

1

al lado derecho

- cos (\frac{k}{2}) + 1 = 0.25

Restar

1

de ambos lados

- cos (\frac{k}{2}) + 1 - 1 = 0.25 - 1

Simplificar

- cos (\frac{k}{2}) = - 0.75

- cos (\frac{k}{2}) = - 0.75

Dividir ambos lados entre

- 1

- cos (\frac{k}{2}) = - 0.75

Dividir ambos lados entre

- 1

\frac{- cos ( \frac{k}{2} )}{- 1} = \frac{- 0.75}{- 1}

Simplificar

cos (\frac{k}{2}) = 0.75

cos (\frac{k}{2}) = 0.75

Aplicar propiedades trigonométricas inversas

cos (\frac{k}{2}) = 0.75

Soluciones generales para

cos (\frac{k}{2}) = 0.75

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{k}{2} = arccos (0.75) + 2 πn, \frac{k}{2} = 2 π - arccos (0.75) + 2 πn

\frac{k}{2} = arccos (0.75) + 2 πn, \frac{k}{2} = 2 π - arccos (0.75) + 2 πn

Resolver

\frac{k}{2} = arccos (0.75) + 2 πn : k = 2 arccos (0.75) + 4 πn

\frac{k}{2} = arccos (0.75) + 2 πn

Multiplicar ambos lados por

2

\frac{k}{2} = arccos (0.75) + 2 πn

Multiplicar ambos lados por

2

\frac{2 k}{2} = 2 arccos (0.75) + 2 \cdot 2 πn

Simplificar

k = 2 arccos (0.75) + 4 πn

k = 2 arccos (0.75) + 4 πn

Resolver

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn : k = 4 π - 2 arccos (0.75) + 4 πn

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn

Multiplicar ambos lados por

2

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn

Multiplicar ambos lados por

2

\frac{2 k}{2} = 2 \cdot 2 π - 2 arccos (0.75) + 2 \cdot 2 πn

Simplificar

k = 4 π - 2 arccos (0.75) + 4 πn

k = 4 π - 2 arccos (0.75) + 4 πn

k = 2 arccos (0.75) + 4 πn, k = 4 π - 2 arccos (0.75) + 4 πn

Mostrar soluciones en forma decimal

k = 2 \cdot 0.72273 \dots + 4 πn, k = 4 π - 2 \cdot 0.72273 \dots + 4 πn

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