web viewtides. amount of daylight. energy waves. sine graph: fill in the important points using...
TRANSCRIPT
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?
For : c affects horizontal translationd affects the vertical translation
For : a affects vertical stretch and |a| is the amplitude.
b affects the period. Period ¿2π|b|
General function:
Solutions:
State the transformations which map , and state the amplitude, period and principal axis for:
a) b)
c) d)
e) Answers:
a) Horizontal stretch of 1/2, vertical shift of -3amplitude = 1, period = π, principal axis of y = -3
b) Horizontal shift of −π2 , vertical shift of 1
amplitude = 1, period = 2π , principal axis of y = 1c) Horizontal shift of 2, vertical shift of 2, vertical stretch of 2
amplitude = 2, period = 2π , principal axis of y = 2
d) Horizontal stretch of 1/2, horizontal shift of −π4 ,vertical shift of -1
amplitude = 1, period = π, principal axis of y = -1
e) Horizontal stretch of π2 , horizontal shift of π, vertical stretch of
52 ,
vertical shift of -3, amplitude = 52 , period = π2, principal axis of y = -3