Question

Given that cos(theta) = -2 radical 5/5, and is in Quadrant II, what is cos(2theta)?

Answer 1

$cos \theta = \frac{ - 2 \sqrt{5} }{5}$

$cos 2\theta = 2cos {}^{2} \theta - 1 \\ cos2 \theta = 2( \frac{ - 2 \sqrt{5} }{5} ) {}^{2} - 1 \\ cos2 \theta = 2( \frac{20}{ \\ 25} ) - 1 \\ cos2 \theta = \frac{40 - 25}{25} = \frac{15}{25} = \frac{3}{5}$