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Popular >

69cos(T/2)=45

Solución

69 cos (\frac{T}{2}) = 45

Solución

T = 2 \cdot 0.86034 \dots + 4 πn, T = 4 π - 2 \cdot 0.86034 \dots + 4 πn

+1

Grados

T = 98.58858 \dots^{\circ} + 72 0^{\circ} n, T = 621.41141 \dots^{\circ} + 72 0^{\circ} n

Pasos de solución

69 cos (\frac{T}{2}) = 45

Dividir ambos lados entre

69

69 cos (\frac{T}{2}) = 45

Dividir ambos lados entre

69

\frac{69 cos ( \frac{T}{2} )}{69} = \frac{45}{69}

Simplificar

cos (\frac{T}{2}) = \frac{15}{23}

cos (\frac{T}{2}) = \frac{15}{23}

Aplicar propiedades trigonométricas inversas

cos (\frac{T}{2}) = \frac{15}{23}

Soluciones generales para

cos (\frac{T}{2}) = \frac{15}{23}

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

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn, \frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn, \frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

Resolver

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn : T = 2 arccos (\frac{15}{23}) + 4 πn

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn

Multiplicar ambos lados por

2

\frac{T}{2} = arccos (\frac{15}{23}) + 2 πn

Multiplicar ambos lados por

2

\frac{2 T}{2} = 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplificar

\frac{2 T}{2} = 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplificar

\frac{2 T}{2} : T

\frac{2 T}{2}

Dividir:

\frac{2}{2} = 1

= T

Simplificar

2 arccos (\frac{15}{23}) + 2 \cdot 2 πn : 2 arccos (\frac{15}{23}) + 4 πn

2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn

Resolver

\frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn : T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

\frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

Multiplicar ambos lados por

2

\frac{T}{2} = 2 π - arccos (\frac{15}{23}) + 2 πn

Multiplicar ambos lados por

2

\frac{2 T}{2} = 2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplificar

\frac{2 T}{2} = 2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Simplificar

\frac{2 T}{2} : T

\frac{2 T}{2}

Dividir:

\frac{2}{2} = 1

= T

Simplificar

2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{15}{23}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{15}{23}) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

T = 2 arccos (\frac{15}{23}) + 4 πn, T = 4 π - 2 arccos (\frac{15}{23}) + 4 πn

Mostrar soluciones en forma decimal

T = 2 \cdot 0.86034 \dots + 4 πn, T = 4 π - 2 \cdot 0.86034 \dots + 4 πn

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