SOLUTION: Find all solutions in the interval [0, 2π) (increasing order) for the equation below. Enter DNE in any empty blank. 9 cot^3 x = 3 cot x x = x = x = x = x

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions in the interval [0, 2π) (increasing order) for the equation below. Enter DNE in any empty blank. 9 cot^3 x = 3 cot x x = x = x = x = x      Log On


   

Question 931431: Find all solutions in the interval [0, 2π) (increasing order) for the equation below. Enter DNE in any empty blank.
9 cot^3 x = 3 cot x
x =
x =
x =
x =
x =
x =
Thank you
Answer by lwsshak3(11628) About Me  (Show Source):
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Find all solutions in the interval [0, 2π) (increasing order) for the equation below. Enter DNE in any empty blank.
9 cot^3 x = 3 cot x
divide both sides by 3 cot x
3cot^2(x)=1
cot^2(x)=1/3
x=±√(1/3)=±1/√3
x=π/3+2πn,n=any integer
x=2π/3+2πn,n=any integer
x=4π/3+2πn,n=any integer
x=5π/3+2πn,n=any integer