Period and Amplitude Changes of Trigonometric Functions

This applet demonstrates the period and amplitude changes of trigonometric functions such as sine, cosine, and tangent. By adjusting parameters through interactive controls, users can visually observe how the graph transforms vertically (amplitude changes) and horizontally (period changes). The vertical stretch or compression alters the peak and trough values of the function, while horizontal compression or stretching modifies the length of one complete cycle. The tool includes text input fields and interactive buttons that allow students to manipulate key parameters in real time and immediately see the corresponding effects on the function's graph. This dynamic, visual approach helps learners develop a deep, intuitive understanding of how each parameter in a trigonometric function influences its graphical shape. The applet is designed to support high school mathematics courses covering trigonometric functions, providing an engaging exploratory environment where students can test hypotheses, make observations, and connect algebraic expressions with their geometric representations. Through repeated interaction, students learn to predict how changes in amplitude and period affect the wave pattern before making any adjustments, strengthening both their conceptual knowledge and problem-solving skills.