document.write( "Question 413727: sin2x=-2sinx \n" ); document.write( "

Algebra.Com's Answer #290560 by jsmallt9(3759) $\"\"$ $\"About$

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sin(2x) = -2sin(x)
\n" ); document.write( "First let's use the sin(2x) formula so we have everything in terms of just x:
\n" ); document.write( "2sin(x)cos(x) = -2sin(x)
\n" ); document.write( "Now we'll add 2sin(x) to each side:
\n" ); document.write( "2sin(x)cos(x) + 2sin(x) = 0
\n" ); document.write( "And then factor out the GCF which is 2sin(x):
\n" ); document.write( "2sin(x)(cos(x) + 1) = 0
\n" ); document.write( "From the Zero Product Property we know that one of these factors must be zero. So:
\n" ); document.write( "2sin(x) = 0 or cos(x) + 1 = 0
\n" ); document.write( "Dividing the first equation by 2 and subtracting 1 from the second equation we get:
\n" ); document.write( "sin(x) = 0 or cos(x) = -1
\n" ); document.write( "So the solutions will by any value for x that makes the sin zero or the cos -1. If you know your special angles you know that 0, $\"pi\"$ and any angle coterminal with them will make sin zero. And $\"pi\"$ and any angle coterminal with it will make cos -1. To express this algebraically we use:
\n" ); document.write( "x = 0 + 2 $\"pi\"$ n
\n" ); document.write( "or
\n" ); document.write( "x = $\"pi\"$ + 2 $\"pi\"$ n
\n" ); document.write( "where \"n\" is any integer. (This is how we include \"all the angles coterminal with...\") (We only need one equation for the angles that are coterminal with $\"pi\"$ . If you don't know what a radian is or if you want an answer in degrees then change the $\"pi\"$ to 180 and the 2 $\"pi\"$ to 360. \n" ); document.write( "

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