document.write( "Question 853174: how many values of x are in the interval [0,2pi] for the equation 2cosx=tanx \n" ); document.write( "

Algebra.Com's Answer #514175 by stanbon(75887) $\"\"$ $\"About$

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how many values of x are in the interval [0,2pi] for the equation
\n" ); document.write( "2cosx=tanx
\n" ); document.write( "------
\n" ); document.write( "2cos(x) = sin(x)/cos(x)
\n" ); document.write( "2cos^2(x) = sin(x)
\n" ); document.write( "2(1-sin^2(x)) = sin(x)
\n" ); document.write( "----
\n" ); document.write( "2sin^2(x) + sin(x) -2 = 0
\n" ); document.write( "-------
\n" ); document.write( "sin(x) = [-1 +- sqrt(1 - 4*2*-2)]/4
\n" ); document.write( "-------
\n" ); document.write( "sin(x) = [-1 +- sqrt(17)]/4
\n" ); document.write( "-------
\n" ); document.write( "sin(x) = (-1-sqrt(17))/4 = -1/28 (extraneous since -1<= sin(x) <=))
\n" ); document.write( "-------
\n" ); document.write( "sin(x) = (-1+sqrt(17))/4 = 0.7808
\n" ); document.write( "====================================
\n" ); document.write( "x = arcsin(0.7808) = 0.8959 radians
\n" ); document.write( "OR
\n" ); document.write( "x = arcsin(0.7808) = (pi-0.8959) = 2.2456 radians
\n" ); document.write( "====================================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "==============
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