Honors Algebra 2: Series, Trigonometry, and Probability

Johns Hopkins University via Coursera

Go to class Write review

Details

Go to class

Provider

Coursera
Pricing

Paid Course
Languages

English
Certificate

Paid Certificate Available
Duration & workload

18 hours 24 minutes
Sessions

On-Demand
Subtitles

English

Found in

Part of

Honors Algebra 2

Overview

Coursera Flash Sale

40% Off Coursera Plus for 3 Months!

Grab it

Honors Algebra 2: Sequences, Series, Trigonometry, & Probability is the fourth part of a four-part specialization, an engaging, application-focused course that explores how algebra connects to patterns, prediction, and data-driven decision-making. Designed for high school students, college-prep learners, and adult learners refreshing their skills, this course is aligned with the Common Core State Standards and is ideal for independent study through Coursera. You’ll begin by analyzing sequences and series, uncovering the structure of arithmetic and geometric patterns and using them to model real-world phenomena like interest growth and population trends. The course then transitions to trigonometry, starting with the fundamental relationships in right triangles. You will master the core trigonometric ratios of sine, cosine, and tangent and their reciprocals. Building on this foundation, you’ll explore key trigonometric identities and use them to simplify complex expressions and solve equations. This understanding culminates in exploring trigonometric functions on the unit circle, revealing them as powerful tools for describing periodic behavior—essential in science, engineering, and even music and design. From there, you’ll shift into introductory probability and statistics, learning how to quantify uncertainty, interpret two-way tables, and distinguish between theoretical and experimental results. In the data analysis portion, you’ll evaluate datasets, calculate measures of central tendency and variability, and draw informed conclusions—skills essential in today’s data-driven world. Whether you're interested in STEM, business, or simply making sense of the information around you, this course provides a deep yet accessible look at how algebra helps you describe, analyze, and predict the world around you. With interactive learning and a clear, concept-driven approach, you'll build a strong foundation for future math courses and practical applications alike.

Syllabus

Sequences and Series

In this module, we will explore the world of sequences and series—ordered lists of numbers and the sums formed from them. You’ll learn to recognize patterns, write formulas, and make predictions using different types of sequences. We’ll focus on two of the most common: arithmetic sequences, where each term increases or decreases by a constant amount, and geometric sequences, where each term is multiplied by the same factor. We’ll also explore recursive sequences, which define each term based on the ones before it, and see how sequences and series can be used to model real-world situations. These ideas lay the groundwork for more advanced mathematical topics you'll encounter later in algebra and beyond.

Angles and the Unit Circle

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.

Trigonometric Functions

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.

Probability

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.