document.write( "Question 512396: need help graphing through at least one period
\n" ); document.write( "and how to find amplitude, phase shift, vertical shift, period\r
\n" ); document.write( "\n" ); document.write( "y=-2+csc((1/2)x+(pi/4)) \n" ); document.write( "

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need help graphing through at least one period
\n" ); document.write( "and how to find amplitude, phase shift, vertical shift, period
\n" ); document.write( "y=-2+csc((1/2)x+(pi/4))
\n" ); document.write( "**
\n" ); document.write( "standard form of equation for csc function: y=csc(Bx-C), period=2π/B, phase shift=C/B
\n" ); document.write( "For given equation:-2+csc((1/2)x+π/4))
\n" ); document.write( "B=1/2
\n" ); document.write( "Period=2π/(1/2)=4π
\n" ); document.write( "Phase shift=C/B=π/4/(1/2)=π/2 (to the left)
\n" ); document.write( "Vertical shift=2 units down
\n" ); document.write( "..
\n" ); document.write( "Graphing:
\n" ); document.write( "Without horizontal and vertical phase shifts,
\n" ); document.write( "you can plot the basic csc(x/2) curve with the following coordinates:
\n" ); document.write( "(0, asymptote), (π,1), (2π, asymptote), (3π,-1), (4π, asymptote)
\n" ); document.write( "shifting curve π/2 to the left:
\n" ); document.write( "(-π/2, asymptote), (π/2, 1), (3π/2, asymptote), (5π/2,-1), (7π/2,asymptote)
\n" ); document.write( "Dropping curve 2 units down: (final configuration)
\n" ); document.write( "(-π/2, asymptote), (π/2, -1), (3π/2, asymptote), (5π/2,-3), (7π/2,asymptote) \n" ); document.write( "

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