Aim:

Understand how changing a sin or cos by adding inside/outside or multiplying inside/outside, change the shape of the graph.

Success:

Can sketch transformed trig graphs, and can determine the parameters of transformed graphs.

Date:
Time Remaining:

https://cuckoo.team/jaytch_ea

Summary of Graphing Transformations

	Outside	Inside
Addition	“Vertical Offset” sin(x)+O shifts up or down (plus goes up)	“Phase Angle” or “Horizontal Shift” sin(x+P) shifts left or right (plus goes left)
Multiplication	“Amplitude” A*sin(x) stretches up or down (bigger than 1 grows vertically)	“Frequency” sin(F*x) stretches in or out (bigger than 1 gets faster stretching in) Frequency = 360/period

Walkthrough of constructing a basic Desmos graph:

1. Type sin(x)

2. Type A*sin(Fx+P)+O

3. Press the blue “all” button to make sliders for each variable

4. Press the wrench to edit the settings, select “Degrees”, xmax=380, xstep=45, ymin=-3.1, ymax=4.1, ystep=1, disable minor gridlines, enable projector mode

5. Type (-P,O) to make a draggable point

6. Start question 1.1 with these values: A=1, F=1, P=0, c=O

Graphing Transformations Further Ex.'s

sin(x) Exercises	cos(x) Exercises
3.1 solo practice 3.2 solo practice 3.3 sin(x)+3, sin(x-90) 3.4 3sin(x+180), 3sin(x-180) 3.5 pairs challenge 3.6 -sin(2x), -2sin(x)+2	4.1 solo practice 4.2 solo practice 4.3 cos(x)+1, cos(x-90) 4.4 -cos(x/2), 3cos(x)-1 4.5 pairs challenge 4.6 2+cos(2x-90),-2cos(x+45)-1

Solo Practice: practice posing and answering your own questions, explore!

Pairs Challenge: in pairs, one writes an equation (in secret!) and graphs it, the other has to work out from the graph what the equation was. Swap...