Question

Зная что cost = -5/13,pi/2

Answer 1

Ответ:

$\cos(t) = - \frac{5}{13} \\ \sin(t) = \sqrt{1 - \cos {}^{2} (t) } = \\ = \sqrt{1 - \frac{25}{169} } = \sqrt{ \frac{144}{169} } = \frac{12}{13}$

$\sin(t - \frac{\pi}{6} ) = \\ = \sin(t) \cos( \frac{\pi}{6} ) - \cos(t) \sin( \frac{\pi}{6} ) = \\ = \frac{ \sqrt{3} }{2} \times \frac{12}{13} - ( - \frac{5}{13} ) \times \frac{1}{2} = \\ = \frac{12 \sqrt{3} + 5}{26}$

$\cos(t - \frac{\pi}{2} ) = \sin(t) = \frac{12}{13}$