SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
18 + 9 cos(2x) = 27 cos(x)
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-> SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
18 + 9 cos(2x) = 27 cos(x)
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Question 1044750: Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
18 + 9 cos(2x) = 27 cos(x) Found 2 solutions by Cromlix, advanced_Learner:Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website! Hi there,
18 + 9 cos(2x) = 27 cos(x)
Replace cos(2x) with 2cos^2(x) -1.
18 + 9(2cos^2(x) - 1) = 27cos(x)
Multiply out.
18 + 18cos^2(x) - 9 = 27cos(x)
Rearrange into quadratic form:
ax^2 + bx + c = 0
18cos^2(x) - 27cos(x)+ 9 = 0
Divide throughout by 9
2cos^2(x) - 3cos(x) + 1 = 0
(2cos(x) - 1)(cos(x) - 1) = 0
2cos(x) - 1 = 0
2cos(x) = 1
cos(x) = 1/2
x = π/3,5π/3
cos(x) - 1 = 0
cos(x) = 1
x = 0, 2π
............
0: π/3:5π/3:2π
Hope this helps :-)
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