document.write( "Question 1156517: Please help me to answer this! Thank you :\r
\n" ); document.write( "\n" ); document.write( "5 + 2cos x - 8sin^2 x = 0 \n" ); document.write( "

Algebra.Com's Answer #779238 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+5+%2B+2cos%28x%29+-+8%2Asin%5E2%28x%29+=+0+\"$
\n" ); document.write( "Use identity:
\n" ); document.write( " $\"+sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1+\"$
\n" ); document.write( " $\"+sin%5E2%28x%29+=+1+-+cos%5E2%28x%29+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( " $\"+5+%2B+2cos%28x%29+-+8%2A%28+1+-+cos%5E2%28x%29%29+=+0+\"$
\n" ); document.write( " $\"+5+%2B+2cos%28x%29+-+8+%2B+8cos%5E2%28x%29+=+0+\"$
\n" ); document.write( " $\"+8cos%5E2%28x%29+%2B+2+cos%28x%29+-+3+=+0+\"$
\n" ); document.write( "Let $\"+cos%28x%29+=+z+\"$
\n" ); document.write( " $\"+8z%5E2+%2B+2z+-+3+=+0+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "Use quadratic formula:
\n" ); document.write( " $\"+z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+8+\"$
\n" ); document.write( " $\"+b+=+2+\"$
\n" ); document.write( " $\"+c+=+-3+\"$
\n" ); document.write( " $\"+z+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A8%2A%28-3%29+%29%29%2F%282%2A8%29+\"$
\n" ); document.write( " $\"+z+=+%28-2+%2B-+sqrt%28+4+%2B+96+%29%29+%2F+16+\"$
\n" ); document.write( " $\"+z+=+%28-2+%2B-+sqrt%28+100+%29%29+%2F+16+\"$
\n" ); document.write( " $\"+z+=+%28+-2+%2B+10+%29+%2F+16+\"$
\n" ); document.write( " $\"+z+=+1%2F2+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+z+=+%28+-2+-+10+%29+%2F+16+\"$
\n" ); document.write( " $\"+z+=+-12%2F16+\"$
\n" ); document.write( " $\"+z+=+-3%2F4+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( " $\"+cos%28x%29+=+z+\"$
\n" ); document.write( " $\"+cos%28x%29+=+1%2F2+\"$
\n" ); document.write( " $\"+x+=+arc+cos%28+1%2F2+%29+\"$
\n" ); document.write( " $\"+x+=+pi+%2F+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x+=+2pi+-+pi%2F3+\"$
\n" ); document.write( " $\"+x+=+%28+5pi+%29%2F3+\"$
\n" ); document.write( "------------------------
\n" ); document.write( " $\"+cos%28x%29+=+z+\"$
\n" ); document.write( " $\"+cos%28x%29+=+-3%2F4+\"$
\n" ); document.write( " $\"+x+=+arc+cos%28+-3%2F4+%29+\"$
\n" ); document.write( " $\"+x+=+138.59+%2A%28+pi+%2F+180+%29+\"$
\n" ); document.write( " $\"+x+=+.77pi+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x+=+%28+360+-+138.59+%29%2A%28+pi+%2F+180+%29+\"$
\n" ); document.write( " $\"+x+=+221.41%2A%28+pi+%2F+180+%29+\"$
\n" ); document.write( " $\"+x+=+1.23pi+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "My answers are:
\n" ); document.write( " $\"+x+=+pi%2F3+\"$
\n" ); document.write( " $\"+x+=+%28+5pi+%29%2F3+\"$
\n" ); document.write( " $\"+x+=+.77pi+\"$
\n" ); document.write( " $\"+x+=+1.23pi+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "I'll check one of the answers. You can check the rest
\n" ); document.write( " $\"+5+%2B+2cos%28x%29+-+8%2Asin%5E2%28x%29+=+0+\"$
\n" ); document.write( " $\"+5+%2B+2%2Acos%28+.77pi+%29+-+8%2Asin%5E2%28+.77pi+%29=+0+\"$
\n" ); document.write( " $\"+5+%2B+%28-1.5%29+-+3.5+=+0+\"$
\n" ); document.write( " $\"+0+=+0+\"$
\n" ); document.write( "Looks OK
\n" ); document.write( "To convert back to degrees, multiply answers by $\"+180%2Fpi+\"$
\n" ); document.write( "Definitely get a 2nd opinion if needed
\n" ); document.write( "and check my math
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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