In this module, you’ll dive into the geometry of circles and triangles to uncover patterns that shape much of trigonometry. You’ll start by learning how to measure angles in both degrees and radians, and see how they show up in right triangles and around a circle. From there, you’ll explore the unit circle, a simple but powerful tool that connects angles to points on the coordinate plane. Using it, you’ll discover how the values of sine, cosine, and tangent repeat in predictable cycles, and why these patterns are so important. By the end of the module, you’ll not only be able to measure and interpret angles with confidence, but also see how this knowledge sets the stage for understanding the periodic functions that model real-world phenomena like sound waves, seasonal patterns, and circular motion.

Now that you’ve seen how the unit circle connects angles to coordinates, you’re ready to extend these ideas into full trigonometric functions. In this module, you’ll learn how sine, cosine, and tangent can be defined for any real number and understood as functions with their own inputs and outputs. You’ll explore their graphs and see how they repeat in predictable cycles, a property called periodicity. Along the way, you’ll uncover how key features like amplitude, period, and phase shift control the shape of these graphs. Most importantly, you’ll see why trigonometric functions matter: they describe patterns we encounter every day, from the orbit of planets to the changing seasons, the vibration of a guitar string, and even the rhythm of your heartbeat. By the end of the module, you’ll be able to graph these functions, explain their behavior, and recognize how they model repeating patterns in the real world.

In this module, you’ll explore the mathematics of chance and uncertainty, and learn how probability helps us make sense of the unpredictable. You’ll begin by calculating the likelihood of simple and compound events, using logic, data, and counting techniques to reason through problems. From there, you’ll practice using tools like two-way tables and Venn diagrams to uncover relationships between events and determine whether they are independent or dependent. You’ll also be introduced to probability distributions, which connect probability to functions and provide a powerful way to describe real-world situations such as rolling dice, drawing cards, or predicting weather patterns. By the end of the module, you’ll not only be able to compute probabilities with confidence, but also understand how probability supports better decision-making in science, business, and everyday life.