document.write( "Question 165355: Solve 2sin^2x = sinx for all real values in the interval (0,2pi) \n" ); document.write( "
Algebra.Com's Answer #121886 by gonzo(654)\"\" \"About 
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2 * sin^2(x) = sin(x)
\n" ); document.write( "dividing both sides of equation by sin(x) gets:
\n" ); document.write( "(2* sin^2(x))/sin(x) = 1
\n" ); document.write( "dividing both sides of eqution by 2 gets:
\n" ); document.write( "sin^2(x)/sin(x) = 1/2
\n" ); document.write( "since sin^2(x) = sin(x) * sin(x), equation becomes:
\n" ); document.write( "(sin(x)*sin(x))/sin(x) = 1/2
\n" ); document.write( "which becomes:
\n" ); document.write( "sin(x) = 1/2
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\n" ); document.write( "if sin(x) = 1/2, then x = 30 degrees.
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\n" ); document.write( "since sin(x) = hypotenuse / y value on the graph, and since hypotenuse is always positive, and since y value on the graph is positive in quadrants 1 and 2, then sin (180-x) = sin(x).
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\n" ); document.write( "since 180-30 = 150, then x can be either 30 degrees or 150 degrees.
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\n" ); document.write( "using the calculator to prove the answer is correct.
\n" ); document.write( "sin (30) = 1/2
\n" ); document.write( "sin (150) = 1/2
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\n" ); document.write( "calculator confirms logic and answer is good.
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