Question

If cos x = −1/3 , find sin(2x) given sin x < 0

Answer 1

$\huge\underline\bold\red{★Answer★}$

$cos(x) = - \frac{1}{3} \\ \sin(x) = \sqrt{1 - {cos}^{2} x} \\ \implies \sin(x) = \sqrt{1 - \frac{1}{9} } \\ = \frac{ \sqrt{8} }{3} \\ \\ sin2x = 2sinxcosx \\ = 2 \frac{ \sqrt{8} }{3} ( - \frac{1}{3} ) \\ = - \frac{2 \sqrt{8} }{9}$