Question

Вычислите значение тригонометрических функций

Answer 1

Пошаговое объяснение:

$tg\beta =-3\ \ \ \ \ \frac{\pi }{2}<\beta <\pi \ \ \ \ sin\beta =? \ \ \ \ cos\beta =?\ \ \ \ ctg\beta =?\\tg^2\beta =(-3)^2=9\\\frac{sin^2\beta }{cos^2\beta}=9\\sin^2\beta =9*cos^2\beta \\9*sin^2\beta +sin^2\beta =9*sin^2\alpha +9*cos^2\beta \\10*sin^2\beta =9*(sin^2\beta +cos^2\beta )\\10*sin^2\beta =9\ |:10\\sin^2\beta =\frac{9}{10} \\sin\beta =б\sqrt{\frac{9}{10} } =б\frac{3}{\sqrt{10} } =б\frac{3\sqrt{10} }{10}.\\\frac{\pi }{2}<\beta <\pi\ \ \ \ \ \Rightarrow$

$sin\beta =\frac{3\sqrt{10} }{10}.\\cos^2\beta =1-sin^2\beta =1-\frac{9}{10} =\frac{1}{10}. \\cos\beta =б\sqrt{\frac{1}{10} }=б\frac{1}{\sqrt{10} }=б\frac{\sqrt{10} }{10}. \\\frac{\pi }{2}<\beta <\pi\ \ \ \ \Rightarrow\\cos\beta =-\frac{\sqrt{10} }{10} .\\ctg\beta =\frac{1}{tg\beta } =\frac{1}{-3}=-\frac{1}{3} .$