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:
What is the period? Amplitude?
Cosine Graph:
Fill in the important points using exact angles and heights:
What is the period? Amplitude?
What is the period? Amplitude? Vertical asymptotes?
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:
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
