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5+3cos(1/2 x)=7

Solución

5 + 3 cos (\frac{1}{2} x) = 7

Solución

x = 2 \cdot 0.84106 \dots + 4 πn, x = 4 π - 2 \cdot 0.84106 \dots + 4 πn

Grados

x = 96.37937 \dots^{\circ} + 72 0^{\circ} n, x = 623.62062 \dots^{\circ} + 72 0^{\circ} n

Pasos de solución

5 + 3 cos (\frac{1}{2} x) = 7

Mover

5

al lado derecho

5 + 3 cos (\frac{1}{2} x) = 7

Restar

5

de ambos lados

5 + 3 cos (\frac{1}{2} x) - 5 = 7 - 5

Simplificar

3 cos (\frac{1}{2} x) = 2

3 cos (\frac{1}{2} x) = 2

Dividir ambos lados entre

3

3 cos (\frac{1}{2} x) = 2

Dividir ambos lados entre

3

\frac{3 cos ( \frac{1}{2} x )}{3} = \frac{2}{3}

Simplificar

cos (\frac{1}{2} x) = \frac{2}{3}

cos (\frac{1}{2} x) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (\frac{1}{2} x) = \frac{2}{3}

Soluciones generales para

cos (\frac{1}{2} x) = \frac{2}{3}

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

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn, \frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn, \frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn

Resolver

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn : x = 2 arccos (\frac{2}{3}) + 4 πn

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn

Multiplicar ambos lados por

2

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn

Multiplicar ambos lados por

2

2 \cdot \frac{1}{2} x = 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{1}{2} x = 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2} x

Eliminar los terminos comunes:

2

= x \cdot 1

Multiplicar:

x \cdot 1 = x

= x

Simplificar

2 arccos (\frac{2}{3}) + 2 \cdot 2 πn : 2 arccos (\frac{2}{3}) + 4 πn

2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn

Resolver

\frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn : x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

\frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn

Multiplicar ambos lados por

2

\frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn

Multiplicar ambos lados por

2

2 \cdot \frac{1}{2} x = 2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{1}{2} x = 2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2} x

Eliminar los terminos comunes:

2

= x \cdot 1

Multiplicar:

x \cdot 1 = x

= x

Simplificar

2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{2}{3}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn, x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

Mostrar soluciones en forma decimal

x = 2 \cdot 0.84106 \dots + 4 πn, x = 4 π - 2 \cdot 0.84106 \dots + 4 πn

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2cos^2(x)-15cos(x)+7=0

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