document.write( "Question 839010: 5cos^2 theta +cos theta-1=0 Find all possible values of theta in between 0° and 360° \n" ); document.write( "

Algebra.Com's Answer #505494 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use a substitution and the quadratic formula,
\n" ); document.write( " $\"u=cos%28theta%29\"$
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\n" ); document.write( " $\"5u%5E2%2Bu-1=0\"$
\n" ); document.write( " $\"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"u+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A5%2A%28-1%29+%29%29%2F%282%2A5%29+\"$
\n" ); document.write( " $\"u+=+%28-1+%2B-+sqrt%28+1%2B20+%29%29%2F%2810%29+\"$
\n" ); document.write( " $\"u+=+%28-1+%2B-+sqrt%28+21+%29%29%2F%2810%29+\"$
\n" ); document.write( "First solution:
\n" ); document.write( " $\"u+=+%28-1+%2B+sqrt%28+1%2B20+%29%29%2F%2810%29=+0.3583\"$
\n" ); document.write( " $\"cos%28theta%29=0.3583\"$
\n" ); document.write( " $\"theta=69.0\"$
\n" ); document.write( "Second solution:
\n" ); document.write( " $\"u+=+%28-1+-+sqrt%28+1%2B20+%29%29%2F%2810%29=+-0.5583\"$
\n" ); document.write( " $\"cos%28theta%29=-0.5583\"$
\n" ); document.write( " $\"theta=123.9\"$ \n" ); document.write( "

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