Trigonometry: The Math Behind Motion
Course Length: 1 Semester (15 weeks) Credit: 0.50 Grade Level: 10–12 Prerequisite: Algebra II Course: 270411
Course Length: 1 Semester (15 weeks) Credit: 0.50 Grade Level: 10–12 Prerequisite: Algebra II Course: 270411
What do roller coasters, ocean waves, Ferris wheels, and even music have in common? They all move in patterns—and those patterns can be understood through trigonometry! In Trigonometry 1: The Math Behind Motion, students will explore the exciting world of angles, waves, and circular motion, learning how trigonometry explains the movement we see all around us.
This one-semester course is perfect for students who have completed Algebra 2 and are ready to go deeper into the math that powers science, engineering, and everyday life. Rather than memorizing random formulas, students will explore why trigonometry works—starting with the basics of right triangles and expanding into the world of unit circles, sine and cosine curves, and real-world modeling. You’ll never look at a swinging pendulum or rotating fan the same way again!
We begin the course by reviewing the building blocks: ratios in right triangles (sine, cosine, and tangent), how to find missing side lengths or angles, and how to solve triangles using the Pythagorean Theorem and trigonometric relationships. Then, students step into the world of the unit circle—a powerful tool that links angles and coordinates in a beautiful, circular way. This lays the foundation for understanding periodic motion, like tides or sound waves.
From there, students will explore graphing trigonometric functions. You’ll discover how changing a number in an equation affects the shape of a wave—its height, frequency, and position on the graph. You’ll even learn how to write your own sine and cosine equations to describe things that repeat, like heartbeats or daylight hours throughout the year.
What makes this course fun and practical is the way it connects math to real-life experiences. You might measure the height of a tree using just a protractor and a little trig. You’ll learn how architects design roofs and ramps, how physicists study light and sound, and how engineers model motion in machines. There's even a bit of astronomy, art, and music theory mixed in!
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Algebra 2
the end of the course, students will be able to: 1. Use and prove key trigonometric identities (e.g., angle-sum, double-angle). 2. Solve trigonometric equations, including those involving inverse functions. 3. Model real-world periodic behavior using trig functions. 4. Solve non-right triangles using the Law of Sines and Law of Cosines. 5. Represent and manipulate vectors algebraically and geometrically. 6. Graph and convert between polar and rectangular coordinate systems. 7. Apply trigonometric concepts to model motion, forces, and waves.
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language
English
Duration
00h 00mLevel
beginner
Expiry period
4 Months
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