Question

Помогите сделать не могу!!!

Answer 1

Ответ:

4

$\sin( \frac{5\pi}{4} ) + \sin( \frac{7\pi}{4} ) = \sin(\pi + \frac{\pi}{4} ) + \sin(2\pi - \frac{\pi}{4} ) = \\ = - \sin( \frac{\pi}{4} ) - \sin( \frac{\pi}{4} ) = - 2 \times \frac{ \sqrt{2} }{2} = - \sqrt{2}$

5

$\sin( \alpha ) = \frac{5}{13}$

угол принадлежит 2 четверти, косинус отрицательный

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

$8)\sin( 2\alpha ) = 2 \sin( \alpha ) \cos( \alpha ) = \\ = 2 \times \frac{5}{13} \times ( - \frac{12}{13} ) = - \frac{120}{169}$

$9) \cos( 2\alpha ) = { \cos }^{2} \alpha - { \sin }^{2} \alpha = \\ = \frac{144}{169} - \frac{25}{169} = \frac{119}{169}$

$10)tg2 \alpha = \frac{ \sin( 2\alpha ) }{ \cos( 2\alpha ) } = - \frac{120}{169} \times \frac{169}{119} = - \frac{120}{119}$

$5) \sin( \frac{ \alpha }{2} ) = + - \sqrt{ \frac{1 - \cos( \alpha ) }{2} } \\ \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 + \frac{12}{13} }{2} } = \sqrt{ \frac{25}{13} \times \frac{1}{2} } = \\ = \frac{5}{ \sqrt{26} } = \frac{5 \sqrt{26} }{26}$

$6) \cos ( \frac{ \alpha }{2} ) = + - \sqrt{ \frac{1 + \cos( \alpha ) }{2} } \\ \cos( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \frac{12}{13} }{2} } = \sqrt{ \frac{1}{13} \times \frac{1}{2} } = \\ = \frac{1}{ \sqrt{26} } = \frac{ \sqrt{26} }{26}$

$7)tg( \frac{ \alpha }{2} ) = \frac{ \sin( \frac{ \alpha }{2} ) }{ \cos( \frac{ \alpha }{2} ) } = \frac{5}{ \sqrt{26} } \times \sqrt{26} = 5$