Graphing Transformations Sin Cos

photo credit

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...

S4 Graphing Transformations Sin Cos

By Jay Teach

Made with Slides.com

S4 Graphing Transformations Sin Cos

  • 65

More from Jay Teach