document.write( "Question 972252: Find, to the nearest degree, the roots of cos2θ-2cosθ=0 on the interval 0<θ<360 \n" ); document.write( "

Algebra.Com's Answer #594592 by lwsshak3(11628) $\"\"$ $\"About$

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Find, to the nearest degree, the roots of cos2θ-2cosθ=0 on the interval 0<θ<360
\n" ); document.write( "***
\n" ); document.write( "cos2θ-2cosθ=0
\n" ); document.write( "cos^2(θ)-sin^2(θ)-2cos(θ)
\n" ); document.write( "cos^2(θ)-1+cos^2(θ)-2cos(θ)=0
\n" ); document.write( "2cos^2(θ)-2cosθ-1=0
\n" ); document.write( "solve for cosθ by quadratic formula:
\n" ); document.write( " $\"cos%28theta%29+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "a=2, b=-2, c=-1
\n" ); document.write( "cosθ=1.336 (reject, (-1 < cosx < 1)
\n" ); document.write( "or
\n" ); document.write( "cosθ=-0.366
\n" ); document.write( "θ=111.469˚, 248.13˚ \n" ); document.write( "

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