Trigonometric Functions and Their Graphs

Connecting trigonometric functions to real-world periodic phenomena.; Understanding the Unit Circle as the foundation for sine and cosine.; Exploring the basic graphs of y = sin(x) and y = cos(x) and their key features.; Analyzing the impact of Amplitude (A) on vertical stretching/compression and reflection.; Investigating the effect of Period (B) on horizontal stretching/compression.; Examining Phase Shift (C) as a horizontal translation.; Understanding Vertical Shift (D) as a vertical translation and midline adjustment.; Synthesizing the General Form: y = A sin(Bx - C) + D or y = A cos(Bx - C) + D.; Practical guide to identifying key features from a given trigonometric equation.; Step-by-step strategy for graphing transformed sine and cosine functions.; Detailed examples of sine and cosine transformations.; Analytical review of parameter effects on complex trigonometric functions.; Discussing real-world applications of trigonometric functions and their transformations.