Question

найти синус .........​

Answer 1

Ответ:

$\frac{5 \sqrt{17} }{21}$

Пошаговое объяснение:

Сначала найдём косинус

$\cos( \alpha ) = \frac{ab}{ |a| \times |b| }$

$ab = 2 \times 2 + ( -2 ) \times 3 + 1 \times 6 = 4 - 6 + 6 = 4$

$|a| = \sqrt{ {2}^{2} + {( - 2)}^{2} + {1}^{2} } = \\ = \sqrt{4 + 4 + 1} = \sqrt{9} = 3$

$|b| = \sqrt{ {2}^{2} + {3}^{2} + {6}^{2} } = \\ = \sqrt{4 + 9 + 36} = \sqrt{49} = 7$

$\cos( \alpha ) = \frac{4}{3 \times 7} = \frac{4}{21}$

${ \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} = 1 \\ { \sin( \alpha ) }^{2} = 1 - { \cos( \alpha ) }^{2} \\ \sin( \alpha ) = \sqrt{1 - { \cos( \alpha ) }^{2} } = \sqrt{1 - { (\frac{4}{21}) }^{2} } = \\ = \sqrt{1 - \frac{16}{441} } = \sqrt{ \frac{425}{441} } = \frac{5 \sqrt{17} }{21}$