Question

sabendo que cos x = 2/3 e π/2 < x < π, o valor de sen é:

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Answer 1

$\sin {}^{2} \beta + \cos {}^{2} \beta = 1 \\ \\ \sin {}^{2} \beta + ( \frac{2}{3} ) {}^{2} = 1 \\ \\ \sin {}^{2} \beta + \frac{4}{9} = 1 \\ \\ \sin {}^{2} \beta = 1 - \frac{4}{9} \\ \\ \sin {}^{2} \beta = \frac{9 - 4}{ 9} \\ \\ \sin {}^{2} \beta = \frac{5}{9} \\ \\ \sin \beta = \sqrt{ \frac{5}{9} } \\ \\ \sin \beta = + \frac{ \sqrt{5} }{3}$