SOLUTION: Find the sin(x) if cos(2x)=2/3, with x terminating in quadrant III

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Question 675749: Find the sin(x) if cos(2x)=2/3, with x terminating in quadrant III
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
replace cos%282x%29 with 1-2%2Asin%5E2%28x%29
1-2sin%5E2%28x%29=2%2F3
-2sin%5E2%28x%29=2%2F3-1
-2sin%5E2%28x%29=-1%2F3
2sin%5E2%28x%29=1%2F3

sin%5E2%28x%29=1%2F6
sin%28x%29=+sqrt%281%2F6%29
since sin%28x%29 is negative in quad III, solution is sin%28x%29=+-sqrt%281%2F6%29=-0.408
x=-24.08 degrees
or
x=180-%28-24.08%29=180%2B24.08=204.08 degrees.....in quadrant III