Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION
10 sin2 x = 10 + 5 cos x
x=?
Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO?
2016-06-24 11:42 am
回答 (2)
2016-06-24 12:14 pm
10 sin²(x) = 10 + 5 cos(x)
2 sin²(x) = 2 + cos(x)
2 [1 - cos²(x)] = 2 + cos(x)
2 - 2 cos²(x) = 2 + cos(x)
2 cos²(x) + cos(x) = 0
cos(x) [2 cos(x) + 1] = 0
cos(x) = 0 or cos(x) = -1/2
x = π/2, 3π/2 or x = π + (π/3), 2π - (π/3)
x = π/2, 4π/3, 3π/2, 5π/3
2 sin²(x) = 2 + cos(x)
2 [1 - cos²(x)] = 2 + cos(x)
2 - 2 cos²(x) = 2 + cos(x)
2 cos²(x) + cos(x) = 0
cos(x) [2 cos(x) + 1] = 0
cos(x) = 0 or cos(x) = -1/2
x = π/2, 3π/2 or x = π + (π/3), 2π - (π/3)
x = π/2, 4π/3, 3π/2, 5π/3
2016-06-24 1:05 pm
10 sin^2 x = 10 + 5 cos x
10(1-cos^2 x) = 10 + 5 cos x
10-10cos^2 x -10 - 5 cos x = 0
-10 cos^2 x - 5 cos x = 0
-5 cos x ( 2 cos x + 1) = 0
cos x = 0
x = pi/2, 3pi/2
2 cos x + 1 = 0
2 cos x = -1
cos x = -1/2
x =2pi/3
x = 4pi/3
x=pi/2, 3pi/2, 2pi/3, 4pi/3
10(1-cos^2 x) = 10 + 5 cos x
10-10cos^2 x -10 - 5 cos x = 0
-10 cos^2 x - 5 cos x = 0
-5 cos x ( 2 cos x + 1) = 0
cos x = 0
x = pi/2, 3pi/2
2 cos x + 1 = 0
2 cos x = -1
cos x = -1/2
x =2pi/3
x = 4pi/3
x=pi/2, 3pi/2, 2pi/3, 4pi/3
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