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1)
![cos frac{ pi (8x+7)}{4}= frac{ sqrt{2} }{2} \ \
1)frac{ pi (8x+7)}{4}= frac{ pi }{4}+2 pi k \ \
8x+7= frac{ pi }{4}* frac{4}{ pi }+2 pi k* frac{4}{ pi } \ \
8x+7=1+8k \
8x=1-7+8k \
8x=-6+8k \
x=- frac{6}{8} + frac{8k}{8} \
x=- frac{3}{4}+k, cos frac{ pi (8x+7)}{4}= frac{ sqrt{2} }{2} \ \
1)frac{ pi (8x+7)}{4}= frac{ pi }{4}+2 pi k \ \
8x+7= frac{ pi }{4}* frac{4}{ pi }+2 pi k* frac{4}{ pi } \ \
8x+7=1+8k \
8x=1-7+8k \
8x=-6+8k \
x=- frac{6}{8} + frac{8k}{8} \
x=- frac{3}{4}+k,](https://tex.z-dn.net/?f=cos+frac%7B+pi+%288x%2B7%29%7D%7B4%7D%3D+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%5C++%5C+%0A+1%29frac%7B+pi+%288x%2B7%29%7D%7B4%7D%3D+frac%7B+pi+%7D%7B4%7D%2B2+pi+k++%5C++%5C+%0A8x%2B7%3D+frac%7B+pi+%7D%7B4%7D%2A+frac%7B4%7D%7B+pi+%7D%2B2+pi+k%2A+frac%7B4%7D%7B+pi+%7D+++++++%5C++%5C+%0A8x%2B7%3D1%2B8k+%5C+%0A8x%3D1-7%2B8k+%5C+%0A8x%3D-6%2B8k+%5C+%0Ax%3D-+frac%7B6%7D%7B8%7D+%2B+frac%7B8k%7D%7B8%7D++%5C+%0Ax%3D-+frac%7B3%7D%7B4%7D%2Bk%2C++)
где k∈Z
При к=0 х= - ³/₄= - 0,75
![2) frac{ pi (8x+7)}{4}=- frac{ pi }{4}+2 pi k \ \
8x+7=- frac{ pi }{4}* frac{4}{ pi }+2 pi k* frac{4}{ pi } \ \
8x+7=-1+8k \
8x=-1-7+8k \
8x=-8+8k \
x=-1+k, \ 2) frac{ pi (8x+7)}{4}=- frac{ pi }{4}+2 pi k \ \
8x+7=- frac{ pi }{4}* frac{4}{ pi }+2 pi k* frac{4}{ pi } \ \
8x+7=-1+8k \
8x=-1-7+8k \
8x=-8+8k \
x=-1+k, \](https://tex.z-dn.net/?f=2%29+frac%7B+pi+%288x%2B7%29%7D%7B4%7D%3D-+frac%7B+pi+%7D%7B4%7D%2B2+pi+k+%5C++%5C+%0A8x%2B7%3D-+frac%7B+pi+%7D%7B4%7D%2A+frac%7B4%7D%7B+pi+%7D%2B2+pi+k%2A+frac%7B4%7D%7B+pi+%7D+%5C++%5C+%0A8x%2B7%3D-1%2B8k+%5C+%0A8x%3D-1-7%2B8k+%5C+%0A8x%3D-8%2B8k+%5C+%0Ax%3D-1%2Bk%2C+%5C++++++)
где к∈Z.
При к=0 х=-1
Ответ: - 0,75.
2)
![tg frac{ pi (2x+1)}{6}= frac{1}{ sqrt{3} } \ \
frac{ pi (2x+1)}{6}= frac{ pi }{6}+ pi k \ \
2x+1= frac{ pi }{6}* frac{6}{ pi }+ pi k* frac{6}{ pi } \ \
2x+1=1+6k \ 2x=1-1+6k \
2x=6k \
x=3k, tg frac{ pi (2x+1)}{6}= frac{1}{ sqrt{3} } \ \
frac{ pi (2x+1)}{6}= frac{ pi }{6}+ pi k \ \
2x+1= frac{ pi }{6}* frac{6}{ pi }+ pi k* frac{6}{ pi } \ \
2x+1=1+6k \ 2x=1-1+6k \
2x=6k \
x=3k,](https://tex.z-dn.net/?f=tg+frac%7B+pi+%282x%2B1%29%7D%7B6%7D%3D+frac%7B1%7D%7B+sqrt%7B3%7D+%7D+%5C++%5C+%0A+frac%7B+pi+%282x%2B1%29%7D%7B6%7D%3D+frac%7B+pi+%7D%7B6%7D%2B+pi+k+%5C++%5C+%0A2x%2B1%3D+frac%7B+pi+%7D%7B6%7D%2A+frac%7B6%7D%7B+pi+%7D%2B+pi+k%2A+frac%7B6%7D%7B+pi+%7D+%5C++%5C+%0A2x%2B1%3D1%2B6k+%5C+2x%3D1-1%2B6k+%5C+%0A2x%3D6k+%5C+%0Ax%3D3k%2C+++++++)
где к∈Z.
При к= -1 х= -3
Ответ: -3.
3)
![sin frac{ pi (2x-3)}{6}=-0.5 \ \
frac{ pi (2x-3)}{6}=(-1)^{k+1} frac{ pi }{6}+ pi k \ \
2x-3=(-1)^{k+1} frac{ pi }{6}* frac{6}{ pi }+ pi k* frac{6}{ pi } \ \
2x-3=(-1)^{k+1}+6k \
2x=(-1)^{k+1}+3+6k \
x= frac{1}{2}*(-1)^{k+1}+1.5+3k, sin frac{ pi (2x-3)}{6}=-0.5 \ \
frac{ pi (2x-3)}{6}=(-1)^{k+1} frac{ pi }{6}+ pi k \ \
2x-3=(-1)^{k+1} frac{ pi }{6}* frac{6}{ pi }+ pi k* frac{6}{ pi } \ \
2x-3=(-1)^{k+1}+6k \
2x=(-1)^{k+1}+3+6k \
x= frac{1}{2}*(-1)^{k+1}+1.5+3k,](https://tex.z-dn.net/?f=sin+frac%7B+pi+%282x-3%29%7D%7B6%7D%3D-0.5+%5C++%5C+%0A+frac%7B+pi+%282x-3%29%7D%7B6%7D%3D%28-1%29%5E%7Bk%2B1%7D+frac%7B+pi+%7D%7B6%7D%2B+pi+k+%5C++%5C+%0A2x-3%3D%28-1%29%5E%7Bk%2B1%7D+frac%7B+pi+%7D%7B6%7D%2A+frac%7B6%7D%7B+pi+%7D%2B+pi+k%2A+frac%7B6%7D%7B+pi+%7D+%5C++%5C+%0A2x-3%3D%28-1%29%5E%7Bk%2B1%7D%2B6k+%5C+%0A2x%3D%28-1%29%5E%7Bk%2B1%7D%2B3%2B6k+%5C+%0Ax%3D+frac%7B1%7D%7B2%7D%2A%28-1%29%5E%7Bk%2B1%7D%2B1.5%2B3k%2C+++++++)
где к∈Z.
При к= -1 ¹/₂ * (-1)⁻¹⁺¹ + 3*(-1) +1,5= ¹/₂ - 3 +1,5= -1
При к=0 ¹/₂ * (-1) +3*0 +1,5= -0,5 +1,5=1
Ответ: -1.
где k∈Z
При к=0 х= - ³/₄= - 0,75
где к∈Z.
При к=0 х=-1
Ответ: - 0,75.
2)
где к∈Z.
При к= -1 х= -3
Ответ: -3.
3)
где к∈Z.
При к= -1 ¹/₂ * (-1)⁻¹⁺¹ + 3*(-1) +1,5= ¹/₂ - 3 +1,5= -1
При к=0 ¹/₂ * (-1) +3*0 +1,5= -0,5 +1,5=1
Ответ: -1.
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