Question

помогите пожалуйста с тригонометрией
Вариант 17

Answer 1

1.

$75\textdegree = \dfrac{75\pi}{180} = \boldsymbol{\dfrac{5\pi}{12}}$  радиан.

2.

$\sin\alpha \cdot \cos\alpha\cdot \text{tg}\alpha = \sin\alpha\cdot\cos\alpha\cdot\dfrac{\sin\alpha}{\cos\alpha} = \sin\alpha\cdot\sin\alpha = \boldsymbol{\sin^2\alpha}$

3.

$\pi < \alpha < \dfrac{3\pi}{2}\ ,\ \cos\alpha < 0\\\\\\\sin\alpha = -\dfrac{4}{5}\\\\\\\sin^2\alpha + \cos^2\alpha = 1\\\\\\\cos\alpha = -\sqrt{1 - \sin^2\alpha} = - \sqrt{1-\left(-\dfrac{4}{5}\right)^2} = -\sqrt{1-\dfrac{16}{25}} = -\sqrt{\dfrac{9}{25}} = \boldsymbol{-\dfrac{3}{5}}$