document.write( "Question 1121665: Sin theta . Cos theta = 1/2. Solve the following equation for 0< or equal to x < or equal to 2π \n" ); document.write( "

Algebra.Com's Answer #737642 by htmentor(1343) $\"\"$ $\"About$

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For simplicity, let theta = x
\n" ); document.write( "sin(x)cos(x) = 1/2
\n" ); document.write( "Using the identity cos(x) = sqrt(1 - sin^2(x)) we have:
\n" ); document.write( "sin(x)*sqrt(1 - sin^2(x)) = 1/2
\n" ); document.write( "Square both sides:
\n" ); document.write( "sin^2(x)(1 - sin^2(x)) = 1/4
\n" ); document.write( "sin^4(x) - sin^2(x) + 1/4 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "(sin^2(x) - 1/2)(sin^2(x) - 1/2) = 0
\n" ); document.write( "This gives sin(x) = 1/sqrt(2)
\n" ); document.write( "In the interval 0 to 2pi, there are two solutions: x = pi/4 and 5*pi/4 \n" ); document.write( "

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