Free online course Trigonometry

About the free online course

Trigonometry stops being intimidating when you can see how its ideas connect: angles describe turns, circles turn angles into numbers, and identities give you reliable shortcuts to solve problems quickly. This free online course guides you from the basics to the kind of fluency you need for school success, entrance exams, and later math and science courses.

You will start by developing a clear understanding of angles and the ways we measure them. By moving comfortably between degrees and radians, you gain the language used in most advanced topics, including arc length, sector geometry, and motion applications such as angular velocity and linear speed. From there, you’ll learn to recognize coterminal and reference angles so you can simplify expressions and avoid common sign mistakes.

The unit circle becomes a practical tool rather than something to memorize. You’ll connect it to the six trigonometric functions and learn how symmetry, periodic behavior, and reciprocal and quotient relationships help you compute exact values efficiently. Special right triangles reinforce these ideas, building fast recall and strong geometric intuition that translates to test problems and everyday calculations.

As the course progresses, you’ll gain confidence with trigonometric identities, including Pythagorean, cofunction, double-angle, half-angle, and power-reducing formulas. Instead of feeling like a bag of tricks, these methods will start to look like patterns you can choose strategically to rewrite expressions and verify relationships. You’ll also practice solving trigonometric equations, including cases with multiple solutions and multiple angles.

Finally, you’ll see how trigonometry models the world: angle-of-elevation word problems, bearings and navigation, clock-angle reasoning, oblique triangles with the Law of Sines and Law of Cosines, and a bridge into polar and rectangular forms. With steady practice built in, you’ll finish better prepared to approach new trig questions calmly, accurately, and with a plan.