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cos(x/2)=-0.4

Solución

cos (\frac{x}{2}) = - 0.4

Solución

x = 2 \cdot 1.98231 \dots + 4 πn, x = - 2 \cdot 1.98231 \dots + 4 πn

+1

Grados

x = 227.15635 \dots^{\circ} + 72 0^{\circ} n, x = - 227.15635 \dots^{\circ} + 72 0^{\circ} n

Pasos de solución

cos (\frac{x}{2}) = - 0.4

Aplicar propiedades trigonométricas inversas

cos (\frac{x}{2}) = - 0.4

Soluciones generales para

cos (\frac{x}{2}) = - 0.4

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

\frac{x}{2} = arccos (- 0.4) + 2 πn, \frac{x}{2} = - arccos (- 0.4) + 2 πn

\frac{x}{2} = arccos (- 0.4) + 2 πn, \frac{x}{2} = - arccos (- 0.4) + 2 πn

Resolver

\frac{x}{2} = arccos (- 0.4) + 2 πn : x = 2 arccos (- 0.4) + 4 πn

\frac{x}{2} = arccos (- 0.4) + 2 πn

Multiplicar ambos lados por

2

\frac{x}{2} = arccos (- 0.4) + 2 πn

Multiplicar ambos lados por

2

\frac{2 x}{2} = 2 arccos (- 0.4) + 2 \cdot 2 πn

Simplificar

x = 2 arccos (- 0.4) + 4 πn

x = 2 arccos (- 0.4) + 4 πn

Resolver

\frac{x}{2} = - arccos (- 0.4) + 2 πn : x = - 2 arccos (- 0.4) + 4 πn

\frac{x}{2} = - arccos (- 0.4) + 2 πn

Multiplicar ambos lados por

2

\frac{x}{2} = - arccos (- 0.4) + 2 πn

Multiplicar ambos lados por

2

\frac{2 x}{2} = - 2 arccos (- 0.4) + 2 \cdot 2 πn

Simplificar

x = - 2 arccos (- 0.4) + 4 πn

x = - 2 arccos (- 0.4) + 4 πn

x = 2 arccos (- 0.4) + 4 πn, x = - 2 arccos (- 0.4) + 4 πn

Mostrar soluciones en forma decimal

x = 2 \cdot 1.98231 \dots + 4 πn, x = - 2 \cdot 1.98231 \dots + 4 πn

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sin(2x)=10cos(x)

sin (2 x) = 10 cos (x)

-2cos(3θ)=1,0<= θ<= 2pi

- 2 cos (3 θ) = 1, 0 \leq θ \leq 2 π

cos(a)=0.998482

cos (a) = 0.998482