Yes. You can start learning on Learnr for free. Learnr Pro unlocks higher daily limits and extra features.

Learn Trigonometry

From right triangles to the unit circle and waves, one idea at a time.

Free to start. Built from a single prompt. No credit card.

Trigonometry studies the relationships between angles and side lengths, starting with right triangles and the ratios sine, cosine and tangent. It then generalizes those ratios to any angle using the unit circle, which turns them into periodic functions that describe waves, rotation, sound and alternating current. Along the way you learn radians, the graphs of trig functions, identities, inverse functions and the laws of sines and cosines for any triangle. Learnr builds a personalized trigonometry course and teaches it in short interactive lessons with diagrams, so the triangle picture and the unit circle picture connect.

How to learn Trigonometry, step by step

Start with right triangles and SOH CAH TOA. Label opposite, adjacent and hypotenuse relative to the angle you care about, then find missing sides and angles. Practice with real setups like a ladder against a wall or the height of a tree from its shadow.
Learn radians as arc length. Understand that one radian is the angle whose arc equals the radius, so a full turn is 2π radians. Convert common angles until 30, 45, 60 and 90 degrees read naturally as π/6, π/4, π/3 and π/2.
Build the unit circle from two special triangles. Use the 45-45-90 and 30-60-90 triangles to derive the coordinates at each standard angle, then use symmetry and quadrant signs for the rest. Sketch the full circle from memory until it takes only a couple of minutes.
Graph the functions and their transformations. Plot sine and cosine from the unit circle, then see how y = A sin(B(x - C)) + D changes amplitude, period (2π/B), phase shift and midline. Learn why tangent has vertical asymptotes where cosine is zero.
Practice identities and trig equations. Work with Pythagorean, reciprocal, double-angle and sum identities, and solve equations like 2 sin x = 1 over a full interval, remembering the second solution. Short daily Learnr sets keep identities fresh enough to recognize.
Solve general triangles. Use the law of sines for angle-side-angle and side-side-angle cases, watching for the ambiguous case with two possible triangles, and the law of cosines for side-angle-side and side-side-side.

What you'll learn

Solve right triangles with sine, cosine and tangent
Convert between degrees and radians and use the unit circle
Graph trig functions and identify amplitude, period and phase shift
Prove and apply core identities such as sin²θ + cos²θ = 1
Solve any triangle with the law of sines and the law of cosines

What's inside your Trigonometry course

A sample path Learnr builds for Trigonometry. Your real course adapts to your goal and level.

1. Right triangle ratios and SOH CAH TOA
2. Radians and the unit circle
3. Graphs of sine, cosine and tangent
4. Trigonometric identities
5. Inverse trig functions and trig equations
6. Laws of sines and cosines and applications

How long does it take to learn Trigonometry?

With solid algebra and basic geometry, a full trigonometry course takes about 2 to 4 months at 3 to 5 hours a week. Right triangle trigonometry alone can be learned in a couple of weeks, while identities and equations take the most practice.

What you need before you start

Algebra, including solving equations and working with square roots and fractions, plus basic geometry such as the Pythagorean theorem and angle sums in triangles.

Common mistakes to avoid

Leaving a calculator in degree mode when the problem uses radians, or the reverse, which gives confident but wrong answers.
Writing sin(x + y) = sin x + sin y. Trig functions are not linear, so use the sum identities instead.
Stopping at the first solution of an equation like sin x = 1/2, when another angle in the interval also works.

How Learnr builds your course

Type your topic

Tell Learnr you want to learn Trigonometry, or get as specific as you like.

Get a personalized course

Learnr instantly builds a full Trigonometry course tailored to your goal and skill level.

Learn and level up

Move through bite-sized lessons and interactive practice, earning XP and keeping your streak.

Trigonometry questions, answered

Do I need to memorize the unit circle?

You need the values at standard angles available quickly, but it is better to rebuild them from the two special right triangles and quadrant signs. That way you can always reconstruct a value you forget.

Why are radians used instead of degrees?

Radians measure angles by arc length relative to the radius, which makes many formulas simpler. In calculus, the derivative of sin x is cos x only when x is in radians.