SOLUTION: Find the set of values of x (in radians) for which csc(x) = sqrt(2), for x in [0, 2π]

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Question 813094: Find the set of values of x (in radians) for which csc(x) = sqrt(2), for x in [0, 2π]
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28x%29=sqrt%282%29
we know that cosecant is the reciprical of sine so
sin%28x%29+=+1%2Fsqrt%282%29
now rationalize
sin%28x%29+=+sqrt%282%29%2F2
we can tell by this that x=+pi%2F4
but thats not all.
sine is positive in quadrant 1 and 2 so x+=+3pi%2F4.
These types of problems will always have 2 answers.