SOLUTION: Find the solution of the equation in the interval [0,2pi) algebraically. {{{3csc^2x-4=0}}} If I could get some quick help on this it would be greatly appreciated. I got stuc

Algebra ->  Trigonometry-basics -> SOLUTION: Find the solution of the equation in the interval [0,2pi) algebraically. {{{3csc^2x-4=0}}} If I could get some quick help on this it would be greatly appreciated. I got stuc      Log On


   

Question 746599: Find the solution of the equation in the interval [0,2pi) algebraically.
3csc%5E2x-4=0
If I could get some quick help on this it would be greatly appreciated. I got stuck at csc%5E2x=%284%2F3%29 when trying on my own to figure this out.
Found 2 solutions by Alan3354, reviewermath:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the solution of the equation in the interval [0,2pi) algebraically.
3csc%5E2x-4=0
If I could get some quick help on this it would be greatly appreciated. I got stuck at csc%5E2x=%284%2F3%29 when trying on my own to figure this out.
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csc%5E2x=%284%2F3%29
Invert
sin%5E2%28x%29+=+3%2F4
sin(x) = sqrt(3)/2
x = pi/3, 2pi/3

Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
csc%5E2x=%284%2F3%29, get the reciprocal of both sides
%28sin+x%29%5E2+ = 3%2F4, get the square root of both sides
sin x = ±sqrt%283%29%2F2
x = pi%2F3, 2pi%2F3, 4pi%2F3, 5pi%2F3