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August 2022
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Нужно решить уравнение [tex] \sqrt{3} /2 sin3x- \frac{1}{2} cos3x=-1[/tex]
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Swift311
Sqrt(3)/2 заменяем на cos(pi/6) и 1/2 заменяем на sin(pi/6), получим:
cos(pi/6)*sin3x-sin(pi/6)*cos3x=-1
Это формула sin(x-y), получаем:
sin(3x-pi/6)=-1
3x-pi/6=-pi/2+2pi*n
3x=5pi/12+2pi*n
x=5pi/36+2pi*n/3
2 votes
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Answers & Comments
cos(pi/6)*sin3x-sin(pi/6)*cos3x=-1
Это формула sin(x-y), получаем:
sin(3x-pi/6)=-1
3x-pi/6=-pi/2+2pi*n
3x=5pi/12+2pi*n
x=5pi/36+2pi*n/3