См. вложение
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А)sint=-2√2;
t+5π/4+2πk;t+7π/4+2πk;k€Z(где k целое число)
б)соst=0;
2π+2πk,k€Z(где к целое число)
Обрати внимание, что на первом графике нарисованы 3 функции. Не забудь поставить разметку на графиках. Удачи
Привет красотка) как дела?)
Понизим степень косинуса с помощью формулы косинуса двойного угла:
![cos2 \alpha =2cos^2 \alpha -1 \\ \\ cos^2 \alpha = \frac{1}{2} (cos2 \alpha +1)](https://tex.z-dn.net/?f=cos2+%5Calpha+%3D2cos%5E2++%5Calpha+-1+%5C%5C++%5C%5C+cos%5E2++%5Calpha+%3D+%5Cfrac%7B1%7D%7B2%7D+%28cos2+%5Calpha+%2B1%29)
В результате можно будет воспользоваться табличным интегралом от косинуса и степенной функции.
![\int\limits^{ \pi/2}_{- \pi/2} { cos^2 2x} \, dx = \frac{1}{2} \int\limits^{ \pi/2}_{- \pi/2} { (cos 4x+1) } \, dx = \\ \\ =\frac{1}{2} \int\limits^{ \pi/2}_{- \pi/2} { cos 4x} \, dx + \frac{1}{2} \int\limits^{ \pi/2}_{- \pi/2} { } \, dx = \\ \\ = \frac{1}{2} \int\limits^{ \pi/2}_{- \pi/2} { \frac{1}{4} cos 4x} \, d(4x) + \frac{1}{2} \int\limits^{ \pi/2}_{- \pi/2} { } \, dx =](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%7B+cos%5E2+2x%7D+%5C%2C+dx+%3D++%5Cfrac%7B1%7D%7B2%7D+%5Cint%5Climits%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%7B+%28cos+4x%2B1%29+%7D+%5C%2C+dx+%3D+%5C%5C++%5C%5C++%3D%5Cfrac%7B1%7D%7B2%7D+%5Cint%5Climits%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%7B+cos+4x%7D+%5C%2C+dx+%2B+%5Cfrac%7B1%7D%7B2%7D+%5Cint%5Climits%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%7B+%7D+%5C%2C+dx+%3D+%5C%5C++%5C%5C+%3D+%5Cfrac%7B1%7D%7B2%7D+%5Cint%5Climits%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%7B++%5Cfrac%7B1%7D%7B4%7D+cos+4x%7D+%5C%2C+d%284x%29+%2B+%5Cfrac%7B1%7D%7B2%7D+%5Cint%5Climits%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%7B+%7D+%5C%2C+dx+%3D)
![= \frac{1}{8} sin4x|^{ \pi/2}_{- \pi/2} + \frac{1}{2} x|^{ \pi/2}_{- \pi/2} = \\ \\ = \frac{1}{8} (sin4 \frac{\pi}{2} -sin4\frac{-\pi}{2} ) + \frac{1}{2} (\frac{\pi}{2} -\frac{-\pi}{2} ) = \\ \\ \frac{1}{8} (sin2 \pi -sin(-2 \pi) ) + \frac{\pi}{2} = \frac{\pi}{2}](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B1%7D%7B8%7D+sin4x%7C%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%2B+%5Cfrac%7B1%7D%7B2%7D+x%7C%5E%7B+%5Cpi%2F2%7D_%7B-+%5Cpi%2F2%7D+%3D+%5C%5C++%5C%5C+%3D+%5Cfrac%7B1%7D%7B8%7D+%28sin4+%5Cfrac%7B%5Cpi%7D%7B2%7D+-sin4%5Cfrac%7B-%5Cpi%7D%7B2%7D+%29+%2B+%5Cfrac%7B1%7D%7B2%7D+%28%5Cfrac%7B%5Cpi%7D%7B2%7D+-%5Cfrac%7B-%5Cpi%7D%7B2%7D+%29+%3D++%5C%5C++%5C%5C+%5Cfrac%7B1%7D%7B8%7D+%28sin2+%5Cpi+-sin%28-2+%5Cpi%29+%29+%2B+%5Cfrac%7B%5Cpi%7D%7B2%7D+%3D+%5Cfrac%7B%5Cpi%7D%7B2%7D)