Question

Алгебра, 10.

Заполнить таблицу:

Answer 1

sina

$\sin( \frac{11\pi}{3} ) = \sin( 9\pi+ \frac{2\pi}{3} ) = \\ = - \sin( \frac{2\pi}{3} ) = - \frac{ \sqrt{3} }{2} \\ \sin( - \frac{11\pi}{4} ) = \sin( - 3\pi + \frac{\pi}{4} ) = \\ = - \sin( \frac{\pi}{4} ) = - \frac{ \sqrt{2} }{2}$

$\sin( \frac{3\pi}{6} ) = \sin( \frac{\pi}{2} ) = 1 \\ \sin( \frac{20\pi}{3} ) = \sin(7\pi - \frac{\pi}{3} ) = \\ = \sin( \frac{\pi}{3} ) = \frac{ \sqrt{3} }{2} \\ \sin( \frac{55\pi}{4} ) = \sin(14\pi - \frac{\pi}{4} ) = \\ = - \sin( \frac{\pi}{4} ) = - \frac{ \sqrt{2} }{2}$

$\sin( \frac{11\pi}{2} ) = \sin(5\pi + \frac{\pi}{2} ) = - 1 \\ \sin( - \frac{5\pi}{4} ) = \sin( -\pi - \frac{\pi}{4} ) = \\ = \sin( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2}$

$\sin( - \frac{11\pi}{3} ) = \sin( - 9\pi - \frac{2\pi}{3} ) = \\ = \sin( \frac{2\pi}{3} ) = \frac{ \sqrt{3} }{2}$

cosa

$\cos( \frac{11\pi}{3} ) = \cos( \frac{2\pi}{3} ) = \frac{1}{2} \\ \cos( - \frac{11\pi}{4} ) = - \cos( \frac{\pi}{4} ) = - \frac{ \sqrt{2} }{2}$

$\cos( \frac{3\pi}{6} ) = 0 \\ \cos( \frac{20\pi}{3} ) = - \cos( \frac{\pi}{3} ) = - \frac{1}{2}$

$\cos( \frac{55\pi}{4} ) = \cos( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2} \\ \cos( \frac{11\pi}{2} ) = 0$

$\cos( - \frac{5\pi}{4} ) = - \cos( \frac{\pi}{4} ) = - \frac{ \sqrt{2} }{2} \\ \cos( - \frac{11\pi}{3} ) = \cos( \frac{2\pi}{3} ) = \frac{1}{2}$

tga

$tg( \frac{11\pi}{3} ) = - \frac{ \sqrt{3} }{2} \times 2 = - \sqrt{3}$

$tg( - \frac{11\pi}{4} ) = - \frac{ \sqrt{2} }{2} \times ( - \frac{2}{ \sqrt{2} }) = 1$

$tg( \frac{3\pi}{6} )$

не определен

$tg( \frac{20\pi}{3} ) = \frac{ \sqrt{3} }{2} \times ( - 2) = - \sqrt{3}$

$tg( \frac{55\pi}{4} ) = - \frac{ \sqrt{2} }{2} \times \frac{2}{ \sqrt{2} } = - 1 \\ tg( \frac{11\pi}{2} )$

не определен

$tg( - \frac{5\pi}{4} ) = \frac{ \sqrt{2} }{2} \times( - \sqrt{2} ) = - 1 \\ tg( - \frac{11\pi}{ 3} ) = \frac{ \sqrt{3} }{2} \times 2 = \sqrt{3}$

ctga

$ctg( \frac{11\pi}{3} ) = - \frac{ \sqrt{3} }{3} \\ ctg( - \frac{11\pi}{4} ) = 1$

$ctg( \frac{\pi}{2} ) = 0 \\ ctg( \frac{20\pi}{3} ) = - \frac{ \sqrt{3} }{3}$

$ctg( \frac{55\pi}{4} ) = - 1 \\ ctg( \frac{11\pi}{2} ) = 0 \\ ctg( - \frac{5\pi}{4} ) = - 1$

$ctg( - \frac{11\pi}{3} ) = \frac{ \sqrt{3} }{3}$