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