SOLUTION: Find sinƟ if cscƟ = √2

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Question 925007: Find sinƟ if cscƟ = √2
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given: Using x = theta we have
(1) csc(x) = sqrt%282%29
Since sin(x) = 1/csc(x) we have
(3) sin(x) = 1%2Fsqrt%282%29
It's improper to write an expression with a square root in the denominator so let's "fix" (3) as follows;
(4) sin(x) = %281%2Fsqrt%282%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29 wherein we have multiplied (3) by one, thus did not change the value of sin(x). Now simple multiple the numerators of (4) and the denominators of (4) you get
(5) sin(x) = %281%2A%28sqrt%282%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29%29
Note that the denominator of (5) is
(6) sqrt%282%29%2Asqrt%282%29 or simply
(7) 2
Therefore, in proper form we have
(8) sin(x) = sqrt%282%29%2F2