![sin(-{5\pi\over2}+x)=-cosx\\\sqrt2cosxsinx=cosx\\\\cosx=0\\sinx={1\over\sqrt2}\\\\x={\pi\over2}+\pi k, k\in \mathbb {Z}\\x=(-1)^k{\pi\over4}+\pi k, k\in \mathbb {Z}](https://tex.z-dn.net/?f=sin%28-%7B5%5Cpi%5Cover2%7D%2Bx%29%3D-cosx%5C%5C%5Csqrt2cosxsinx%3Dcosx%5C%5C%5C%5Ccosx%3D0%5C%5Csinx%3D%7B1%5Cover%5Csqrt2%7D%5C%5C%5C%5Cx%3D%7B%5Cpi%5Cover2%7D%2B%5Cpi+k%2C+k%5Cin+%5Cmathbb+%7BZ%7D%5C%5Cx%3D%28-1%29%5Ek%7B%5Cpi%5Cover4%7D%2B%5Cpi+k%2C+k%5Cin+%5Cmathbb+%7BZ%7D)
Корни на отрезке <span>[(9пи)/2; 6пи]:
</span>
![x\in\{{9\pi\over2};{19\pi\over4};{11\pi\over2}\}](https://tex.z-dn.net/?f=x%5Cin%5C%7B%7B9%5Cpi%5Cover2%7D%3B%7B19%5Cpi%5Cover4%7D%3B%7B11%5Cpi%5Cover2%7D%5C%7D)
<span>
</span>
∫xcosx .dx=I
u=x, v´=cosx
u´=1, v=sinx
I=xsinx-∫sinxdx=xsinx-(-cosx)=xsinx+cosx
(∫uv´=uv-∫u´v)
<span>49-3х=4 </span>
<span>-3х=4-49 </span>
<span>-3х=-15 </span>
<span>х=15</span>
<span>легко</span>
180:8=22,5
180-22,5=157,5
157,5:2=78,75
Ответ точный!!!
78,75 градусов
X+x/9=2
2x/9=2
2x=2×9
2x=18
x=18/2
x=9
Ответ: x=9.