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Sketch the graph of y=2+3sin(2x+π/4). Include at least 2 full periods. State the period, amplitude, phase shift and vertical shift.
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\n" ); document.write( "Equation for sin function: y=Asin(Bx-C), A=amplitude, period=2π/B, phase shift=C/B
\n" ); document.write( "For given equation: y=2+3sin(2x+π/4)
\n" ); document.write( "Amplitude=3
\n" ); document.write( "B=2
\n" ); document.write( "period=2π/B=2π/2=π
\n" ); document.write( "1/4 period: π/4
\n" ); document.write( "C=π/4
\n" ); document.write( "phase shift=C/B=(π/4)/2=π/8 (shift to the left)
\n" ); document.write( "vertical shift: 2 units up
\n" ); document.write( "..
\n" ); document.write( "Graphing:
\n" ); document.write( "I don't have the means to draw the graph but I will show you how to develop the coordinates with which you can use to draw the graph your self.
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\n" ); document.write( "Coordinates for 2 periods with amplitude=1 and no phase shift: (basic sin curve with period=π
\n" ); document.write( "(0,0), (π/4,1), (π/2,0), (3π/4,-1), (π,0), (5π/4,1), (3π/2,0), (7π/4,-1), (2π,0)
\n" ); document.write( "..
\n" ); document.write( "Increase amplitude=3:
\n" ); document.write( "(0,0), (π/4,3), (π/2,0), (3π/4,-3), (π,0), (5π/4,3), (3π/2,0), (7π/4,-3), (2π,0)
\n" ); document.write( "..
\n" ); document.write( "horizontal shift π/8 to the left:
\n" ); document.write( "(-π/8,0), (π/8,3), (3π/8,0), (5π/8,-3), (7π/8,0), (9π/8,3), (11π/8,0), (13π/8,-3), (15π/8,0)
\n" ); document.write( "..
\n" ); document.write( "vertical shift 2 units up: (final configuration)
\n" ); document.write( "(-π/8,2), (π/8,5), (3π/8,2), (5π/8,-1), (7π/8,2), (9π/8,5), (11π/8,2), (13π/8,-1), (15π/8,2)\r
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