Question

Sabendo que sen² α = 49, α ∈ [0,2 π[, obtenha o valor de cos α.​

Answer 1

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