document.write( "Question 251209: Hi. \r
\n" ); document.write( "\n" ); document.write( "I am trying to solve for x in the following equation:\r
\n" ); document.write( "\n" ); document.write( "2sin(x)=sin(120-x)\r
\n" ); document.write( "\n" ); document.write( "Your help would be greatly appreciated. Thanks.\r
\n" ); document.write( "\n" ); document.write( "-Max \n" ); document.write( "
Algebra.Com's Answer #182959 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
2sin(x)=sin(120-x)

\n" ); document.write( "Generally we can solve an equation if we can solve a Trig. equation if we can transform it into the form:
\n" ); document.write( "q(variable-expression) = number
\n" ); document.write( "where q is one of the Trig functions.

\n" ); document.write( "We have two sin's but with different arguments. SO we cannot combine them into a single function as they stand. So we need to use one of the identities to change the argument. We will use sin(A-B) = sin(A)cos(B) - cos(A)sin(B) giving us:
\n" ); document.write( "2sin(x) = sin(120)cos(x) - cos(120)sin(x)
\n" ); document.write( "Since sin(120) = \"sqrt%283%29%2F2\" and cos(120) = -1/2:
\n" ); document.write( "\"2sin%28x%29+=+%28sqrt%283%29%2F2%29cos%28x%29+-+%28-1%2F2%29sin%28x%29\"
\n" ); document.write( "or
\n" ); document.write( "\"2sin%28x%29+=+%28sqrt%283%29%2F2%29cos%28x%29+%2B+%281%2F2%29sin%28x%29\"
\n" ); document.write( "Subtracting \"%281%2F2%29\"sin(x) from each side we get:
\n" ); document.write( "\"%283%2F2%29sin%28x%29+=+%28sqrt%283%29%2F2%29cos%28x%29\"
\n" ); document.write( "Multiply both sides by 2 to get rid of the fractions:
\n" ); document.write( "\"3sin%28x%29+=+%28sqrt%283%29%29cos%28x%29\"
\n" ); document.write( "Divide both sides by cos(x):
\n" ); document.write( "\"%283sin%28x%29%29%2Fcos%28x%29+=+sqrt%283%29\"
\n" ); document.write( "Since sin(x)/cos(x) = tan(x):
\n" ); document.write( "\"3tan%28x%29+=+sqrt%283%29\"
\n" ); document.write( "Divide both sides by 3:
\n" ); document.write( "\"tan%28x%29+=+sqrt%283%29%2F3\"
\n" ); document.write( "We now have the desired form. This should be a recognizable this value for tan. (If not, use your calculator.)
\n" ); document.write( "x = 30 + 180n
\n" ); document.write( " \n" ); document.write( "
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