document.write( "Question 444050: solve sin(θ)-√(3)cos(θ)=√(3) \n" ); document.write( "

Algebra.Com's Answer #306254 by lwsshak3(11628) $\"\"$ $\"About$

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solve sin(θ)-√(3)cos(θ)=√(3)
\n" ); document.write( "..
\n" ); document.write( "use x for theta
\n" ); document.write( "assume 0< x< 360 deg or 0< x< 2π radians
\n" ); document.write( "sinx-√3cosx=√3
\n" ); document.write( "sinx=√3+√3cosx=√3(1+cosx)
\n" ); document.write( "square both sides
\n" ); document.write( "sin^2x=3(1+2cosx+cos^2x)
\n" ); document.write( "1-cos^2x=3+6cosx+3cos^2x
\n" ); document.write( "4cos^2x+6cosx+2=0
\n" ); document.write( "2cos^2x+3cosx+1=0
\n" ); document.write( "(2cosx+1)(cosx+1)=0
\n" ); document.write( "2cosx+1=0
\n" ); document.write( "cosx=-1/2
\n" ); document.write( "x=120 and 240 deg or 2π/3 and 4π/3 radians
\n" ); document.write( "..
\n" ); document.write( "cosx+1=0
\n" ); document.write( "cosx=-1
\n" ); document.write( "x=180 deg or π radians\r
\n" ); document.write( "\n" ); document.write( "ans:
\n" ); document.write( "x=120, 240, and 180 deg or 2π/3, 4π/3 and π radians \n" ); document.write( "

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