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cos(2a)= 2/3 ,sin(a)

Solución

cos (2 a) = \frac{2}{3}, sin (a)

Solución

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

Pasos de solución

cos (2 a) = \frac{2}{3}, sin (a)

Aplicar propiedades trigonométricas inversas

cos (2 a) = \frac{2}{3}

Soluciones generales para

cos (2 a) = \frac{2}{3}

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

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

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

Resolver

2 a = arccos (\frac{2}{3}) + 2 πn : a = \frac{arccos ( \frac{2}{3} )}{2} + πn

2 a = arccos (\frac{2}{3}) + 2 πn

Dividir ambos lados entre

2

2 a = arccos (\frac{2}{3}) + 2 πn

Dividir ambos lados entre

2

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

Simplificar

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

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

Resolver

2 a = 2 π - arccos (\frac{2}{3}) + 2 πn : a = π - \frac{arccos ( \frac{2}{3} )}{2} + πn

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

Dividir ambos lados entre

2

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

Dividir ambos lados entre

2

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

Simplificar

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

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

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

Soluciones para el rango

sin (a)

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

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