Curve Sketching (1 Viewer)

[nrlwinner]

Hi. I have a quick question.

I know how to sketch something like y=sin2x and y=sin(x+pi)

But what would I do about y=sin(2x+pi)

Do I do the same as y=sin2(x+pi)? Or is it something else?

 

[untouchablecuz]

Hi. I have a quick question.

I know how to sketch something like y=sin2x and y=sin(x+pi)

But what would I do about y=sin(2x+pi)

Do I do the same as y=sin2(x+pi)? Or is it something else?

method 1

y=sin(2x+2pi)

let 2c+2pi=0 => c=-pi

so, this means that we obtain the graph of y=sin(2x+2pi) by shifting the graph y=sin(2x) to the left by pi units

so draw y=sin(2x) (with dotted lines), then proceed to move every point pi units to the left. pay particular attention to the x-intercepts. its as simple as that

method 2

y=sin(2x+2pi) = sin2(x+pi)=sin2(x-(-pi))

so from general graph transformations (replacing x with x-a shifts a graph a units to the right) this graph is obtained by shifting the graph of y=sin2x -pi units to the right i.e. pi units to the left

again, draw y=sin(2x) with dotted lines, and shift it across

so something like y=4cos(4x-67)=4cos4(x-67/4), is obtained by shifting y=cos(4x) 67/4 units to the right

this method is essentially the same to method 1

 

[Drongoski]

sin(2x + 2pi) is immediately sin 2x