Question

решите пожалуйста срочно! ​

Answer 1

Ответ:

1

$\frac{1}{2} \arcsin( \frac{ \sqrt{3} }{2}) - 2\arccos( - \frac{1}{2} ) = \\ = \frac{1}{2} \times \frac{\pi}{3} - 2 \times \frac{\pi}{3} = \frac{\pi}{6} - \frac{2\pi}{ 3} = \\ = \frac{\pi - 4\pi}{6} = - \frac{\pi}{2}$

2

$2\arccos( - \frac{ \sqrt{2} }{2} ) - \frac{1}{3} \arcsin( - \frac{1}{2} ) = \\ = 2 \times \frac{\pi}{4} - \frac{1}{3} \times ( - \frac{\pi}{6} ) = \\ = \frac{\pi}{2} + \frac{\pi}{18} = \frac{10\pi}{18} = \frac{5\pi}{9}$

3

$2\arccos( - \frac{ \sqrt{3} }{2} ) - \arcsin (\frac{1}{2}) = \\ = 2 \times \frac{\pi}{6} - \frac{\pi}{6} = \frac{\pi}{6}$

4

$\sin(2\arccos( \frac{1}{2} ) + 3\arctg( \sqrt{3}) ) = \\ = \sin(2 \times \frac{\pi}{3} + 3 \times \frac{\pi}{3} ) = \sin( \frac{2\pi}{3} + \pi) = \\ = - \sin( \frac{2\pi}{3} ) = - \frac{ \sqrt{3} }{2}$

5

$\ctg(2\arcsin( - \frac{ \sqrt{2} }{2} ) + \arccos( - \frac{1}{2} )) = \\ = \ctg(2 \times ( - \frac{\pi}{4} ) + \frac{\pi}{3} ) = \\ = \ctg( - \frac{\pi}{2} + \frac{ \pi}{3} ) = \ctg( - \frac{\pi}{6} ) = - \sqrt{3}$