document.write( "Question 869656: Use trigonometric identities to solve cos(2θ)+cos(θ)=0 exactly for 0∘≤θ<360∘. If there is more than one answer, enter your answers as a comma separated list. \n" ); document.write( "

Algebra.Com's Answer #524355 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( "So,
\n" ); document.write( " $\"cos%282theta%29%2Bcos%28theta%29=0\"$ can be re-written as
\n" ); document.write( " $\"2%28cos%28theta%29%29%5E2%2Bcos%28theta%29-1=0\"$
\n" ); document.write( "and if we abbreviate it by defining $\"y=cos%28theta%29\"$
\n" ); document.write( "we can re-write it as
\n" ); document.write( " $\"2y%5E2%2By-1=0\"$
\n" ); document.write( "That quadratic equation can be solve by factoring,
\n" ); document.write( "or by completing the square,
\n" ); document.write( "or by using the quadratic formula,
\n" ); document.write( "to yield the solutions
\n" ); document.write( " $\"system%28y=-1%2C%22or%22%2Cy=1%2F2%29\"$ .
\n" ); document.write( "Going back to $\"theta\"$ and for $\"0%5Eo%3C=theta%3C360%5Eo\"$
\n" ); document.write( "we find that $\"y=cos%28theta%29=-1\"$ ---> $\"highlight%28theta=180%5Eo%29\"$
\n" ); document.write( "and $\"y=cos%28theta%29=1%2F2\"$ ---> $\"system%28highlight%28theta=60%5Eo%29%2C%22or%22%2Chighlight%28theta=300%5Eo%29%29\"$ \n" ); document.write( "

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