lkueh.files. web viewthere are several properties or characteristics that can be used to describe...
TRANSCRIPT
![Page 1: lkueh.files. Web viewThere are several properties or characteristics that can be used to describe sinusoidal functions. These include period, amplitude, and phase shift](https://reader036.vdocuments.us/reader036/viewer/2022062907/5ab360c97f8b9ac66c8e3d12/html5/thumbnails/1.jpg)
MCR3U Periodic FunctionsMs. Kueh
A function is periodic if the graph repeats at regular intervals the y-values repeat at regular intervals
A function that describes periodic data can be described as sinusoidal.
A cycle is ______________________________________________________
The period is the horizontal distance of ________________________________
The following function is periodic. Highlight one cycle and state the period.
Example 1 Determine whether the function is periodic. If it is, state the period.a) b)
![Page 2: lkueh.files. Web viewThere are several properties or characteristics that can be used to describe sinusoidal functions. These include period, amplitude, and phase shift](https://reader036.vdocuments.us/reader036/viewer/2022062907/5ab360c97f8b9ac66c8e3d12/html5/thumbnails/2.jpg)
There are several properties or characteristics that can be used to describe sinusoidal functions. These include period, amplitude, and phase shift.
Amplitude – Half the difference between the maximum value of the function and the minimum value of the function.
Axis of the Curve – A horizontal line that is half-way between the maximum and minimum values.
Phase Shift – The horizontal shift of a graph from its original position.
*Phase shift depends on the original graph – for example the phase shift for a sine graph and a cosine graph are different
![Page 3: lkueh.files. Web viewThere are several properties or characteristics that can be used to describe sinusoidal functions. These include period, amplitude, and phase shift](https://reader036.vdocuments.us/reader036/viewer/2022062907/5ab360c97f8b9ac66c8e3d12/html5/thumbnails/3.jpg)
Example 2 For the following periodic functiona) highlight one cycleb) draw the axis of the curvec) state the period and calculate the amplitude
d) From the graph, what is f (1)? f (5)? f (9)? f (13)?
e) What is f (45)?
For a periodic function, f (x)=f (x ± p) where p is the period.
y=sinθ
Sketch a graph with the main points:
Domain:_______________________________________
Range:________________________________________
Period:________________________________________
Amplitude:_____________________________________
Roots:_________________________________________
![Page 4: lkueh.files. Web viewThere are several properties or characteristics that can be used to describe sinusoidal functions. These include period, amplitude, and phase shift](https://reader036.vdocuments.us/reader036/viewer/2022062907/5ab360c97f8b9ac66c8e3d12/html5/thumbnails/4.jpg)
y=cosθ
Sketch a graph with the main points:
Domain:_______________________________________
Range:________________________________________
Period:________________________________________
Amplitude:_____________________________________
Roots:_________________________________________
What translation would map the graph of y=sinθonto y=cosθ?
y= tanθ
There are certain values of θ for which y= tanθ is undefined. The graph of y=tan θis said to
have asymptotes at these points. Broken vertical lines represent the asymptotes.
Sketch a graph with the main points:
Domain:_______________________________________
Range:________________________________________
Period:________________________________________
Roots:_________________________________________
Homework: pg. 289# C3 pg. 290 #1,2, 6, 7, 8(think sine graph), 9, 10, 18
![Page 5: lkueh.files. Web viewThere are several properties or characteristics that can be used to describe sinusoidal functions. These include period, amplitude, and phase shift](https://reader036.vdocuments.us/reader036/viewer/2022062907/5ab360c97f8b9ac66c8e3d12/html5/thumbnails/5.jpg)
Thinking #24, 25, 26, 27