Question

Найти sina+2cosa, если tga=0.4

Answer 1

$tga=0,4\\\\1+tg^2a=\dfrac{1}{cos^2a}\ \ \to \ \ cos^2a=\dfrac{1}{1+cos^2a}=\dfrac{1}{1,16}=\dfrac{25}{29}\\\\sin^2a=1-cos^2a=\dfrac{4}{29}\\\\a)\ \ a\in (0;\dfrac{\pi}{2}\, ):\ \ sina+2cosa=\dfrac{2}{\sqrt{29}}+2\cdot \dfrac{5}{\sqrt{29}}=\dfrac{12}{\sqrt{29}}\\\\b)\ \ a\in (\ \dfrac{\pi}{2}\, ;\pi \ ):\ \ sina+2cosa=\dfrac{2}{\sqrt{29}}-2\cdot \dfrac{5}{\sqrt{29}}=-\dfrac{8}{\sqrt{29}}$

$c)\ \ a\in (\, \pi \, ;\ \dfrac{3\pi}{2}\, ):\ \ sina+2cosa=-\dfrac{2}{\sqrt{29}}-2\cdot \dfrac{5}{\sqrt{29}}=-\dfrac{12}{\sqrt{29}}\\\\d)\ \ a\in (\ \dfrac{3\pi}{2}\, ;\, 2\pi \, ):\ \ sina+2cosa=-\dfrac{2}{\sqrt{29}}+2\cdot \dfrac{5}{\sqrt{29}}=\dfrac{8}{\sqrt{29}}$