Sin x + √3 cos x =0 Решить уравнение. Created by gurdovaayna. algebra-ru

Sin x + √3 cos x =0 Решить уравнение...

ruslank1460

$Sinx+\sqrt{3}Cosx=0$

Разделим обе части на Cosx ≠ 0 .

$\frac{Sinx}{Cosx}+\frac{\sqrt{3}Cosx }{Cosx}=0\\\\tgx+\sqrt{3}=0\\\\tgx=-\sqrt{3}\\\\x=arctg(-\sqrt{3})+\pi n,n\in z\\\\x=-arctg\sqrt{3}+\pi n,n\in z\\\\x=-\frac{\pi }{3}+\pi n,n\n z$

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Universalka

Verified answer

Обе части уравнения разделим на cosx, где cosx≠0

sin x + √3 cos x = 0|:cosx

tgx + √3 = 0;

tgx = -√3;

x = arctg(-√3) + πn, n∈Z;

x = -π/3 + πn, n∈Z.

Ответ: -π/3 + πn, n∈Z.

11 votes Thanks 29

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