1. Periodic Functions Exploring Sine and Cosine Graphs
Hr. Adv. Algebra II with Trigonometry
Mrs. Stacey

2. Essential Stuff Essential Question What is a periodic function?
Essential Vocabulary
Periodic Function
Amplitude
Period
Parent Function

3. Terminology
Periodic Functions: A function that repeats y-values at regular intervals.
Cycle: One complete pattern of a periodic function.
Period: The horizontal length of one cycle of a periodic function.

4. Periodic Functions
One
Cycle
Period

5. Amplitude 1 2 ( 𝑚𝑎𝑥− min ) or 𝑎 𝟏 𝟐 (𝟔− −𝟒 ) Amplitude = 5
The amplitude of a periodic function is half the difference between the maximum and minimum values of the function.
1 2 ( 𝑚𝑎𝑥− min ) or 𝑎
Maximum = 6
𝟏 𝟐 (𝟔− −𝟒 )
Amplitude = 5
Minimum = -4

6. Parent Functions The parent functions for Sine and Cosine are
𝒚=𝒂𝒔𝒊𝒏𝒃 𝒙−𝒉 +𝒌
𝒚=𝒂𝒄𝒐𝒔𝒃 𝒙−𝒉 +𝒌
𝒙 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕𝒔 𝒕𝒉𝒆 𝒂𝒏𝒈𝒍𝒆 𝜽

7. Period and “b” 𝑷𝒆𝒓𝒊𝒐𝒅= 𝟐𝝅 𝒃 The Period of a Sine and Cosine graph is
𝑷𝒆𝒓𝒊𝒐𝒅= 𝟐𝝅 𝒃
“b” represents the number of
cycles or complete patterns
in the interval from 𝟎 𝒕𝒐 𝟐𝝅

8. Homework: Exploring Sine and Cosine Functions