SOLUTION: What are the x's of: ((sin^2)x) +(cos)x) +1)) = 0

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Question 747135: What are the x's of: ((sin^2)x) +(cos)x) +1)) = 0
Answer by KMST(5397) About Me  (Show Source):
You can put this solution on YOUR website!
%28cos%28x%29%29%5E2%2B%28sin%28x%29%29%5E2=1 --> %28sin%28x%29%29%5E2=1-%28cos%28x%29%29%5E2 so
%28sin%28x%29%29%5E2%2Bcos%28x%29%2B1=0 --> 1-%28cos%28x%29%29%5E2%2Bcos%28x%29%2B1=0 --> -%28cos%28x%29%29%5E2%2Bcos%28x%29%2B2=0 --> %28cos%28x%29%29%5E2-cos%28x%29-2=0
Calling cos%28x%29=y we can re-write the equation as
y%5E2-y-2=0 --> %28y%2B1%29%28y-2%29=0
The solutions to that equation are y=2 and y=-1,
but since -1%3C=cos%28x%29%3C=1, y=2 does not yield a solution of the original
equation.
Looking for solutions between 0%5Eo and 360%5Eo (between 0 and 2piradians),
y=cos%28x%29=-1 --> x=180%5Eo (or x=pi radians)
All solutions can be written as
x=%282k%2B1%29%2A180%5Eo (or x=%282k%2B1%29%2Api if measuring angles in radians)