document.write( "Question 541717: I.Find the amplitude, period, and phase shift of the function
\n" ); document.write( "II. Sketch the graph\r
\n" ); document.write( "\n" ); document.write( "A. \"+y+=-2cos%281%2F4%29x+\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "B. \"+y=-%281%2F2%29sin%282x-%28pi%2F3%29%29+\" \n" ); document.write( "
Algebra.Com's Answer #354395 by lwsshak3(11628)\"\" \"About 
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I.Find the amplitude, period, and phase shift of the function
\n" ); document.write( "II. Sketch the graph\r
\n" ); document.write( "\n" ); document.write( "A. y =-2cos(1/4)x
\n" ); document.write( "Equation for graphing cos function: y=Acos(Bx-C), A=amplitude, Period=2π/B, Phase Shift=C/B.
\n" ); document.write( "For given function:
\n" ); document.write( "y=-2cos((1/4)x-0)
\n" ); document.write( "amplitude=2
\n" ); document.write( "B=1/4
\n" ); document.write( "Period=2π/B=2π/(1/4)=8π
\n" ); document.write( "1/4 period=2π
\n" ); document.write( "Phase shift: none
\n" ); document.write( "..
\n" ); document.write( "Graph function for one period:
\n" ); document.write( "On an xy coordinate system with the x-axis scaled in radians:
\n" ); document.write( "For basic cos function, plot coordinates as follows:
\n" ); document.write( "(0,1), (2π,0), (4π,-1), (6π,0), (8π,1)
\n" ); document.write( "multiply y-coordinates by -2 for final configuration of graph
\n" ); document.write( "(0,-2), (2π,0), (4π,2), (6π,0), (8π,-2)
\n" ); document.write( "..
\n" ); document.write( "B. y=-(1/2)sin(2x-(π/3))
\n" ); document.write( "Equation for graphing sin function: y=Asin(Bx-C), A=amplitude, Period=2π/B, Phase Shift=C/B.
\n" ); document.write( "for given sin function
\n" ); document.write( "amplitude=1/2
\n" ); document.write( "B=2
\n" ); document.write( "Period=2π/2=π
\n" ); document.write( "1/4 period=π/4
\n" ); document.write( "C=π/3
\n" ); document.write( "Phase shift: C/B=(π/3)/2=π/6 (shift to right)
\n" ); document.write( "..
\n" ); document.write( "On an xy coordinate system with the x-axis scaled in radians:
\n" ); document.write( "For basic sin function, plot coordinates as follows:
\n" ); document.write( "(0,0), (π/4,1), (π/2,0), (3π/4,-1), (π,0)
\n" ); document.write( "multiply y-coordinates by -1/2
\n" ); document.write( "(0,0), (π/4,-1/2), (π/2,0), (3π/4,1/2), (π,0)
\n" ); document.write( "shift x-coordinates π/6 units to the right (add π/6 to x coordinates)
\n" ); document.write( "(π/6,0), (5π/12,-1/2), (2π/3,0), (11π/12,1/2), (7π/6,0)
\n" ); document.write( "..
\n" ); document.write( "y-intercept
\n" ); document.write( "y=-(1/2)sin(2x-(π/3))
\n" ); document.write( "x=0
\n" ); document.write( "y=-(1/2)sin(-π/3)=-(1/2)*sin(-π/3)=-(1/2)*(-√3/2)=.433
\n" ); document.write( "..
\n" ); document.write( "Final configuration: (extend curve back to y-intercept)
\n" ); document.write( "(0,4.33), (π/6,0), (5π/12,-1/2), (2π/3,0), (11π/12,1/2), (7π/6,0)
\n" ); document.write( "..
\n" ); document.write( "You now have the coordinates you need to plot the graphs of given functions> \n" ); document.write( "
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