document.write( "Question 62148: Hope you can help me:
\n" ); document.write( "Solve sin2y = cos4y for y, where 0 <= y < 360 \n" ); document.write( "

Algebra.Com's Answer #42902 by joyofmath(189) $\"\"$ $\"About$

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Solve sin2y = cos4y for y, where 0 <= y < 360\r
\n" ); document.write( "\n" ); document.write( "Let x = 2y. Then, $\"sinx+=+cos2x\"$ .
\n" ); document.write( "There's a trig identity: $\"cos2x+=+1-2%28sinx%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "We use that identity and get: $\"sin%28x%29+=+1-2%28sinx%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "Let some variable, say g, = sinx.\r
\n" ); document.write( "\n" ); document.write( "Then, $\"g+=+1-2g%5E2\"$ .
\n" ); document.write( "Or, $\"2g%5E2%2Bg+=+1\"$
\n" ); document.write( "Or, $\"2g%5E2%2Bg-1+=+0\"$ .
\n" ); document.write( "This factors into $\"%282g-1%29%28g%2B1%29+=+0\"$ .
\n" ); document.write( "So, $\"g=1%2F2\"$ or $\"g=-1\"$ .\r
\n" ); document.write( "\n" ); document.write( "So, since $\"g+=+sinx\"$ , $\"sinx+=+1%2F2\"$ or $\"sinx+=+-1\"$ .\r
\n" ); document.write( "\n" ); document.write( "Since x = 2y, $\"sin%282y%29+=+1%2F2\"$ or $\"sin%282y%29+=+-1\"$ .
\n" ); document.write( "So, 2y = 270 degress or 2y = 30 degrees.
\n" ); document.write( "So, the answer is y = 135 degrees or y = 15 degrees.\r
\n" ); document.write( "\n" ); document.write( "Let's verify the answer:\r
\n" ); document.write( "\n" ); document.write( "sin(2*135) = sin(270) = -1 and cos(4*135) = cos(540) = cos(180) = -1.
\n" ); document.write( "sin(2*15) = sin(30) = 1/2 and cos(60) = 1/2. \n" ); document.write( "

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