Graphing a Sine Curve

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Graphing a Sine Curve

• start it end it
• chop it in 4
• slide it up or down
• sketch the wave
• easy as p

how to graph y sin 2 (x p / 4) - 1 in four
easy steps
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Here's what we know
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Here's What We'll Do
1 - find where it starts at h and ends at h
period 2 - chop the interval into 4 equal parts 3
- slide it up or down according to k and a 4 -
draw the curve.
h
h 2p / b
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Step 1 start it end it
y a sin b ( x h ) k parameters h and b are
the horizontal sliders we set the horizontal
sliders first
On the x-axis, we'll start at h, then slide 2p /
b units right
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Step 1 start it end it horizontal sliders

• y sin 2 ( x p/4 ) 1
• phase shift h - p/4
• slide the initial point p/4 units left
• period 2p / b 2p / 2 p
• slide p units right to cycle's end

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horizontal sliders setting up the X-axis
y sin 2 ( x p/4 ) 1

• mark the initial point on the x-axis, (-p/4)
• slide to cycle's end p units right (-p/4 p
  3p/4)

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Step 2 chop it in 4
y sin 2 ( x p/4 ) 1

• find the mid point of the interval
• find the mid points of the two intervals

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Step 3Slide it up or down
y 1 sin 2 ( x p/4 ) 1
parameters a and k are the vertical sliders

• vertical translation k -1
• slide the x-axis down 1 unit
• amplitude a 1
• curve rises 1 unit to max
• curve falls 1 unit to min
• max k a 0, min k - a -2,

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Step 3 Slide it up or downSetting up the Y- axis
y 1 sin 2 ( x p/4 ) 1
p / 4
p / 2
3 p / 4
- p / 4
0

• slide the x-axis down to y -1
• mark the max at (0, 0),
• the min at (p / 2, - 2)
• mark the 3 points where the curve is "on axis".

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Step 4Sketch the Curve
y sin 2 ( x p/4 ) 1
p / 4
p / 2
3 p / 4
- p / 4

• since a gt 0, the curve rises to maximum (0, 0)
• then moves back to the horizontal axis y -1
• then down to min at (p/2, -2)
• then moves back to the horizontal axis y -1
• Click your mouse for the summary

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Graphing a Sine Curve summary

• on the x-axis, find " h " cycle's initial point.
• on the x-axis find cycle's end point (2p / b)
  h.
• chop that interval into 4 equal parts.
• slide the horizontal axis up or down k units.on
  axis are cycle's initial, mid and end points.
  min k a, max k a, plot them .
• sketch away.