document.write( "Question 458991: I've tried multiple ways, but just can't get the answer.
\n" ); document.write( "Please help!\r
\n" ); document.write( "\n" ); document.write( "Solve for x in the interval (0,360), sin(1/2)x = sin(x) \n" ); document.write( "

Algebra.Com's Answer #314826 by htmentor(1343) $\"\"$ $\"About$

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Solve for x in the interval (0,360), sin(1/2)x = sin(x)
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\n" ); document.write( " $\"sin%28x%2F2%29+=+sin%28x%29\"$
\n" ); document.write( "We can write this as
\n" ); document.write( " $\"sin%28x%2F2%29+-+sin%28x%29+=+0\"$
\n" ); document.write( "Let $\"w+=+x%2F2\"$
\n" ); document.write( "Then the equation becomes
\n" ); document.write( " $\"sin%28w%29+-+sin%282w%29+=+0\"$
\n" ); document.write( "Using the double-angle formula $\"sin%282w%29+=+2sin%28w%29cos%28w%29\"$ , we have:
\n" ); document.write( " $\"sin%28w%29+-+2sin%28w%29cos%28w%29+=+0\"$
\n" ); document.write( "Pull out $\"sin%28w%29\"$ :
\n" ); document.write( " $\"sin%28w%29%281+-+2+cos%28w%29%29+=+0\"$
\n" ); document.write( "The RHS will equal 0 if $\"sin%28w%29+=+0\"$ or $\"1+-+2cos%28w%29+=+0\"$
\n" ); document.write( "There is no solution for $\"sin%28w%29+=+0\"$ on the open interval between 0 and 360 deg.
\n" ); document.write( "So we need only to solve $\"1+-+2cos%28w%29+=+0\"$
\n" ); document.write( "This gives $\"cos%28w%29+=+1%2F2\"$
\n" ); document.write( "So w = 60 deg.
\n" ); document.write( "This means x = 2w = 120 deg.
\n" ); document.write( "Ans: x = 120 deg.
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