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katia2101
@katia2101
November 2021
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допоможіть розв'язати тригонометричне рівняння
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Удачник66
Verified answer
3sin^2 (2x) + 10sin (2x) + 3 = 0
Замена sin 2x = y, по определению синуса -1 <= y <= 1
3y^2 + 10y + 3 = 0
(y + 3)(3y + 1) = 0
1) y = sin 2x = -3 - не подходит
2) y = sin 2x = -1/3
2x1 = -arcsin (1/3) + 2pi*k
x1 = -1/2*arcsin (1/3) + pi*k
2x2 = pi + arcsin (1/3) + 2pi*n
x2 = pi/2 + 1/2*arcsin (1/3) + pi*n
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Answers & Comments
Verified answer
3sin^2 (2x) + 10sin (2x) + 3 = 0Замена sin 2x = y, по определению синуса -1 <= y <= 1
3y^2 + 10y + 3 = 0
(y + 3)(3y + 1) = 0
1) y = sin 2x = -3 - не подходит
2) y = sin 2x = -1/3
2x1 = -arcsin (1/3) + 2pi*k
x1 = -1/2*arcsin (1/3) + pi*k
2x2 = pi + arcsin (1/3) + 2pi*n
x2 = pi/2 + 1/2*arcsin (1/3) + pi*n