![Page 1: Periodic Functions - WordPress.com · 2013. 4. 11. · Circular Functions 1.5 Y -1.5 Circular Functions 1.5 Y ( 294, o. .4) (66. , 0.4) 360 Enter y = cosx and y = 0.4 into the GDC,](https://reader036.vdocuments.site/reader036/viewer/2022071416/6112af8c90eefa3ea5706cce/html5/thumbnails/1.jpg)
Periodic Functions
Answer all periodic but d)
What are some examples of natural periodic functions in time?
Weather – monthly rain fall, temperature, seasons,
Tides
Amount of daylight
Energy waves
Sine Graph:
Fill in the important points using exact angles and heights:
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What is the period? Amplitude?
Cosine Graph:
Fill in the important points using exact angles and heights:
What is the period? Amplitude?
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![Page 4: Periodic Functions - WordPress.com · 2013. 4. 11. · Circular Functions 1.5 Y -1.5 Circular Functions 1.5 Y ( 294, o. .4) (66. , 0.4) 360 Enter y = cosx and y = 0.4 into the GDC,](https://reader036.vdocuments.site/reader036/viewer/2022071416/6112af8c90eefa3ea5706cce/html5/thumbnails/4.jpg)
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What is the period? Amplitude? Vertical asymptotes?
![Page 6: Periodic Functions - WordPress.com · 2013. 4. 11. · Circular Functions 1.5 Y -1.5 Circular Functions 1.5 Y ( 294, o. .4) (66. , 0.4) 360 Enter y = cosx and y = 0.4 into the GDC,](https://reader036.vdocuments.site/reader036/viewer/2022071416/6112af8c90eefa3ea5706cce/html5/thumbnails/6.jpg)
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What we should notice from the investigation is:
For siny x c d :
c affects horizontal translation
d affects the vertical translation
For siny a b x :
a affects vertical stretch and is the amplitude.
b affects the period. Period
General function: siny a b x c d
Solutions:
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State the transformations which map siny x , and state the amplitude,
period and principal axis for:
a) sin2 3y x b) sin 12
y x
c) 2sin 2 2y x d) sin 2 12
y x
e) 5 2
sin 2 32
y x
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