document.write( "Question 1157544: Solve 12sin^2(w)+7cos(w)−13=0 for all solutions 0 ≤w<2π \n" ); document.write( "

Algebra.Com's Answer #780417 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+12%2Asin%5E2%28w%29+%2B+7%2Acos%28w%29+-+13+=+0+\"$
\n" ); document.write( " $\"+sin%5E2%28w%29+=+1+-+cos%5E2%28w%29+\"$
\n" ); document.write( " $\"+12%2A%28+1+-+cos%5E2%28w%29+%29+%2B+7%2Acos%28w%29+-+13+=+0+\"$
\n" ); document.write( " $\"+12+-+12%2Acos%5E2%28w%29+%2B+7%2Acos%28w%29+-+13+=+0+\"$
\n" ); document.write( " $\"+12%2Acos%5E2%28w%29+-+7%2Acos%28w%29+%2B+1+=+0+\"$
\n" ); document.write( "Let $\"+z+=+cos%28w%29+\"$
\n" ); document.write( " $\"+12z%5E2+-+7z+%2B+1+=+0+\"$
\n" ); document.write( " $\"+%28+4z+-+1+%29%2A%28+3z+-+1+%29+=+0+\"$ ( by looking at it )
\n" ); document.write( " $\"+4z+=+1+\"$
\n" ); document.write( " $\"+z+=+1%2F4+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+3z+=+1+\"$
\n" ); document.write( " $\"+z+=+1%2F3+\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"+cos%28w%29+=+1%2F4+\"$
\n" ); document.write( "The cosine is positive in 1st and 4th quadrants
\n" ); document.write( " $\"+w+=+arc+cos%28+1%2F4+%29+\"$
\n" ); document.write( " $\"+w+=+1.3181+\"$ radians
\n" ); document.write( " $\"+w+=+2pi+-+1.3181+=+4.9651+\"$ radians
\n" ); document.write( "and
\n" ); document.write( " $\"+cos%28w%29+=+1%2F3+\"$
\n" ); document.write( " $\"+w+=+arc+cos%28+1%2F3+%29+\"$
\n" ); document.write( " $\"+w+=+1.2310+\"$ radians
\n" ); document.write( " $\"+w+=+2pi+-+1.2310+=+5.0522+\"$ radians
\n" ); document.write( "----------------------------------------------
\n" ); document.write( "check answers (4)
\n" ); document.write( " $\"+w+=+1.3181+\"$
\n" ); document.write( " $\"+12%2Asin%5E2%28w%29+%2B+7%2Acos%28w%29+-+13+=+0+\"$
\n" ); document.write( " $\"+12%2A.93749+%2B+7%2A.25+-+13+=+0+\"$
\n" ); document.write( " $\"+11.25+%2B+1.75+-+13+=+0+\"$
\n" ); document.write( " $\"+13+-+13+=+0+\"$
\n" ); document.write( "OK
\n" ); document.write( "You can check the other answers
\n" ); document.write( "check the math & get a 2nd opinion if needed
\n" ); document.write( " \n" ); document.write( "

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