document.write( "Question 729916: Solve: cos^2(theta)+ 2sin(theta)=2 \r
\n" ); document.write( "\n" ); document.write( "Please help. I have no Idea what to do. \n" ); document.write( "

Algebra.Com's Answer #446296 by fcabanski(1391) $\"\"$ $\"About$

You can put this solution on YOUR website!
Remember the identity that $\"sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1\"$ . Whenever there is sin or cos squared and the other not squared, it's a good bet to use that identity.

\n" ); document.write( " $\"cos%5E2%28x%29+=+1+-+sin%5E2%28x%29\"$

\n" ); document.write( "The equation becomes $\"1-sin%5E2%28theta%29+%2B+2%2Asin%28theta%29+=+2\"$

\n" ); document.write( "Subtract 2 from both sides.

\n" ); document.write( " $\"-sin%5E2%28theta%29+%2B+2%2Asin%28theta%29+-+1+=+0\"$

\n" ); document.write( "Multiply each term by negative 1.

\n" ); document.write( " $\"sin%5E2%28theta%29-2%2Asin%28theta%29%2B1+=+0\"$

\n" ); document.write( "Substitute $\"sin%28theta%29=x\"$

\n" ); document.write( " $\"x%5E2+-2x+%2B+1+=+0\"$

\n" ); document.write( "That's a quadratic polynomial.

\n" ); document.write( " $\"%28x-1%29%28x-1%29+=+0\"$ so x=1

\n" ); document.write( " $\"x+=+sin%28theta%29+=+1\"$

\n" ); document.write( "Arcsin (1) = 90 degrees. That's only one possible answer, because sin repeats every 2*pi radians (360 degrees). The complete answer is pi + 2*pi*n radians, or 90 + 360n degrees.
\n" ); document.write( "

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
\n" ); document.write( " \n" ); document.write( "

\n" );