2cos(x/3-p/6) = -корень из3

Question

Математика

Davebbon

6 год назад

2cos(x/3-p/6) = -корень из3

ОТВЕТЫ

Trifonovich

Jul 21, 2019

$2\cos\Big(\dfrac x3-\dfrac{\pi}6\Big)=-\sqrt 3\\ \\ \\\cos\Big(\dfrac x3-\dfrac{\pi}6\Big)=-\dfrac{\sqrt 3}2\\ \\ \\1)~~\dfrac x3-\dfrac{\pi}6=\dfrac{5\pi}6+2\pi n\\ \\ \\~~~~~\dfrac x3=\dfrac{\pi}6+\dfrac{5\pi}6+2\pi n\\ \\ \\~~~~~\dfrac x3=\pi+2\pi n\\ \\ \boxed{\boldsymbol{x_1=3\pi+6\pi n;~~n\in Z}}\\ \\ \\2)~~\dfrac x3-\dfrac{\pi}6=-\dfrac{5\pi}6+2\pi m\\ \\ \\~~~~~\dfrac x3=\dfrac{\pi}6-\dfrac{5\pi}6+2\pi m\\ \\ \\~~~~~\dfrac x3=-\dfrac{2\pi}3+2\pi m\\ \\ \boxed{\boldsymbol{x_2=-2\pi+6\pi m;~~m\in Z}}$

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