document.write( "Question 747135: What are the x's of: ((sin^2)x) +(cos)x) +1)) = 0 \n" ); document.write( "

Algebra.Com's Answer #454749 by KMST(5397) $\"\"$ $\"About$

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$\"%28cos%28x%29%29%5E2%2B%28sin%28x%29%29%5E2=1\"$ --> $\"%28sin%28x%29%29%5E2=1-%28cos%28x%29%29%5E2\"$ so
\n" ); document.write( " $\"%28sin%28x%29%29%5E2%2Bcos%28x%29%2B1=0\"$ --> $\"1-%28cos%28x%29%29%5E2%2Bcos%28x%29%2B1=0\"$ --> $\"-%28cos%28x%29%29%5E2%2Bcos%28x%29%2B2=0\"$ --> $\"%28cos%28x%29%29%5E2-cos%28x%29-2=0\"$
\n" ); document.write( "Calling $\"cos%28x%29=y\"$ we can re-write the equation as
\n" ); document.write( " $\"y%5E2-y-2=0\"$ --> $\"%28y%2B1%29%28y-2%29=0\"$
\n" ); document.write( "The solutions to that equation are $\"y=2\"$ and $\"y=-1\"$ ,
\n" ); document.write( "but since $\"-1%3C=cos%28x%29%3C=1\"$ , $\"y=2\"$ does not yield a solution of the original
\n" ); document.write( "equation.
\n" ); document.write( "Looking for solutions between $\"0%5Eo\"$ and $\"360%5Eo\"$ (between $\"0\"$ and $\"2pi\"$ radians),
\n" ); document.write( " $\"y=cos%28x%29=-1\"$ --> $\"x=180%5Eo\"$ (or $\"x=pi\"$ radians)
\n" ); document.write( "All solutions can be written as
\n" ); document.write( " $\"x=%282k%2B1%29%2A180%5Eo\"$ (or $\"x=%282k%2B1%29%2Api\"$ if measuring angles in radians) \n" ); document.write( "

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