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Avery2015
@Avery2015
June 2022
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Срочно!!!!! Решите тригонометрическое уравнение...
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Timoxa987
1) t = cos2x;
2t^2 - 7t + 3 = 0
Получаем корни 0,5 и 3 (3 не подходит)
cos2x = 0,5
2x = + -п/3 + 2пn; x = +- п/6 + пn
2) [0; 3п/2]
а)0 < -п/6 + пn < 3п/2
п/6 < пn < 9п/6 + п/6
1/6 < n < 10/6
n = 1. x= -п/6
б) 0 < п/6 + пn < 3п/2
-п/6 < пn < 8п/6
-1/6 < n < 8/6
n = 0, n= 1; x1= п/6, x2 = 0
Ответ: 1) x= +-п/6 + пn
2) x1= -п/6; x2 = 0; x3 = п/6
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Answers & Comments
2t^2 - 7t + 3 = 0
Получаем корни 0,5 и 3 (3 не подходит)
cos2x = 0,5
2x = + -п/3 + 2пn; x = +- п/6 + пn
2) [0; 3п/2]
а)0 < -п/6 + пn < 3п/2
п/6 < пn < 9п/6 + п/6
1/6 < n < 10/6
n = 1. x= -п/6
б) 0 < п/6 + пn < 3п/2
-п/6 < пn < 8п/6
-1/6 < n < 8/6
n = 0, n= 1; x1= п/6, x2 = 0
Ответ: 1) x= +-п/6 + пn
2) x1= -п/6; x2 = 0; x3 = п/6