SOLUTION: Find all solutions of the equation in the interval [0, 2pi). Round the solution to four decimal places. {{{csc (x) = -3}}} Any explanation of how to obtain would be greatly

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation in the interval [0, 2pi). Round the solution to four decimal places. {{{csc (x) = -3}}} Any explanation of how to obtain would be greatly      Log On


   



Question 1115178: Find all solutions of the equation in the interval [0, 2pi). Round the solution to four decimal places.
csc+%28x%29+=+-3
Any explanation of how to obtain would be greatly appreciated.

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
csc(x) = -3  ====>  1%2Fsin%28x%29 = - 3  ====>  sin(x) = -1%2F3  ====>


In the given interval  [0,2pi)  the last equation has two solutions



x= -arcsin%281%2F3%29+%2B+pi   and  x= -arcsin%281%2F3%29+%2B+2pi.