Graphing a sine curve

Graphing a Sine Curve : 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

Here's what we know : Here's what we know

Slide 3 : 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 + 2p / b h

Step 1: start it – end it : 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

Step 1: start it – end it horizontal sliders : 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

horizontal sliders: setting up the X-axis : horizontal sliders: setting up the X-axis mark the initial point on the x-axis, (-p/4) slide to cycle's end p units right (-p/4 + p = 3p/4) y = sin 2 ( x + p/4 ) – 1

Step 2: chop it in 4 : Step 2: chop it in 4 find the mid point of the interval find the mid points of the two intervals y = sin 2 ( x + p/4 ) – 1

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

Step 3: Slide it up or downSetting up the Y- axis : Step 3: Slide it up or downSetting up the Y- axis 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". p / 4 p / 2 3 p / 4 - p / 4 0 y = 1 sin 2 ( x + p/4 ) – 1

Step 4:Sketch the Curve : Step 4:Sketch the Curve since a > 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 p / 4 p / 2 3 p / 4 - p / 4 y = sin 2 ( x + p/4 ) – 1

Graphing a Sine Curve: summary : 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.