Question

Обчислити

1. cos135⁰
2. stg210⁰
$3. sin \frac{9\pi}{4}$​

Answer 1

Пошаговое объяснение:

$\cos135 = \cos(90 + 45) = \cos(90) \cos(45) - \sin(90) \sin(45) = 0 - 1 \times \frac{ \sqrt{2} }{2} = - \frac{ \sqrt{2} }{2}$

$\tan(210) = \tan(180 + 30 ) = \frac{ \tan(180) + \tan(30) }{1 - \tan(180) \tan(30) } = \frac{0 + \frac{ \sqrt{3} }{3} }{1 - 0} = \frac{ \frac{ \sqrt{3} }{3} }{1} = \frac{ \sqrt{3} }{3}$

$\sin( \frac{9\pi}{4} ) = \sin( \frac{8\pi + \pi}{4} ) = \sin( \frac{8\pi}{4} + \frac{\pi}{4} ) = \sin(2\pi + \frac{\pi}{4} ) = \sin( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2}$