Summary of "Unit 5 1 1 Introduction to Trigonometric Functions"

Main Ideas and Concepts

Introduction to Trigonometric Functions:
The unit focuses on Graphing Trigonometric Functions. Emphasis on identifying patterns in these graphs.
Periodic Nature of Trigonometric Functions:
Trigonometric Functions are periodic, meaning they repeat indefinitely over regular intervals (referred to as "periods"). The concept of periods is likened to school class schedules that cycle daily.
Understanding Periodicity:
A periodic function repeats itself over consistent intervals, which can be in terms of time or distance. The horizontal length of the cycle is defined as the "period."
Graphing Sine and Cosine Functions:
The Sine Function demonstrates a complete cycle that goes up and down, returning to its starting point. The Cosine Function starts at a different point, which is a backward shift compared to the Sine Function. Both functions are examples of sinusoidal waves or curves, which are characterized by their repetitive nature.
Key Features of Trigonometric Functions:
Recognition of the crest (the highest point) and trough (the lowest point) in the graphs of sine and cosine functions. Understanding the period involves noting the distance between one crest to the next or one trough to the next.

Identifying Periodicity:
- Look for the repeating pattern in the graph.
- Determine the period by measuring the horizontal distance from one point of repetition (crest or trough) to the next.
Distinguishing Between Sine and Cosine Functions:
- Remember that the Sine Function starts at the origin (0,0) and moves up and down.
- The Cosine Function starts at its maximum value (the crest) and has a different starting point compared to the Sine Function.

Periodic Functions: Functions that repeat over regular intervals.
Crest and Trough: Important features to identify in the graphs.
Sinusoidal Functions: The collective term for sine and cosine functions due to their wave-like nature.