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OVI1320
@OVI1320
July 2022
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найти все решения уравнения sin(x-pi/3) = 0.5
удовлетворяющие неравенству x^2-4pi^2 <0
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Удачник66
Verified answer
Sin(x - pi/3) = 0,5
x - pi/3 = pi/6 + 2pi*n; x = pi/3 + pi/6 + 2pi*n = pi/2 + 2pi*n
x - pi/3 = 5pi/6 + 2pi*m; x = 5pi/6 + pi/3 + 2pi*m = 7pi/6 + 2pi*m
Неравенству x^2 - 4pi^2 < 0 удовлетворяют |x| < 2pi, x ∈ (-2pi; 2pi)
x1 = pi/2; x2 = 7pi/6, x3 = pi/2-2pi = -3pi/2, x4 = 7pi/6-2pi = -5pi/6
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Answers & Comments
Verified answer
Sin(x - pi/3) = 0,5x - pi/3 = pi/6 + 2pi*n; x = pi/3 + pi/6 + 2pi*n = pi/2 + 2pi*n
x - pi/3 = 5pi/6 + 2pi*m; x = 5pi/6 + pi/3 + 2pi*m = 7pi/6 + 2pi*m
Неравенству x^2 - 4pi^2 < 0 удовлетворяют |x| < 2pi, x ∈ (-2pi; 2pi)
x1 = pi/2; x2 = 7pi/6, x3 = pi/2-2pi = -3pi/2, x4 = 7pi/6-2pi = -5pi/6