Question

ПОМОГИТЕ! НУЖНО ВЫЧИСЛИТЬ

sina, cosa, tga ctga, если a=П/6+П/4

Answer 1

Ответ:

$\sin( \alpha ) = \sin( \frac{\pi}{6} + \frac{\pi}{4} ) = \\ = \sin( \frac{\pi}{6} ) \cos( \frac{\pi}{4} ) + \cos( \frac{\pi}{6} ) \sin( \frac{\pi}{4} ) = \\ = \frac{1}{2} \times \frac{ \sqrt{2} }{2} + \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{2} }{2} = \\ = \frac{ \sqrt{2} + \sqrt{2} \sqrt{3} }{4} = \frac{ \sqrt{2} (1 + \sqrt{3} )}{4}$

$\cos( \alpha ) = \cos( \frac{\pi}{6} + \frac{\pi}{4} ) = \\ = \cos( \frac{\pi}{6} ) \cos( \frac{\pi}{4} ) - \sin( \frac{\pi}{6} ) \sin( \frac{\pi}{4} ) = \\ = \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{2} }{2} - \frac{1}{2} \times \frac{ \sqrt{2} }{2} = \\ = \frac{ \sqrt{2} ( \sqrt{3} - 1)}{4}$

$tg (\alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \\ = \frac{ \sqrt{2} ( \sqrt{3} + 1)}{4} \times \frac{4}{ \sqrt{2} ( \sqrt{3} - 1)} = \\ = \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1}$

$ctg( \alpha ) = \frac{1}{tg( \alpha )} = \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1}$