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

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

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.

Periodic Functions One Cycle Period

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

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

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

Homework: Exploring Sine and Cosine Functions