Trigonometry: an interactive trigonometry course

Trigonometry is an interactive trigonometry course that goes from naming the sides of a right-angled triangle to the unit circle, trig graphs and identities. Its 35 short sections cover SOH CAH TOA, finding missing sides and angles, degrees and radians, the sine and cosine rules and the area of any triangle, with sliders, explorers and practice questions throughout.

It is built for students meeting trig for the first time and for anyone who learned SOH CAH TOA by rote and now wants to see why it works.

What the trigonometry course covers

Right-angled triangles

The first dozen sections are the trigonometry most people need: naming the sides relative to an angle, choosing sine, cosine or tangent from the two sides involved, then rearranging to find a side or using inverse trig to find an angle. The course adds a built-in check: the opposite side can never be longer than the hypotenuse.

Beyond triangles

Radians and the unit circle extend sine and cosine to any angle, including negative ones and angles over 360°. The point on the unit circle at angle θ is (cos θ, sin θ), which explains the signs in each quadrant, the shape of the sine and cosine waves, and the Pythagorean identity in one picture.

Any triangle

The final part handles triangles without a right angle. The sine rule links each side to the sine of its opposite angle, the cosine rule generalises Pythagoras, and ½ab sin C gives the area without the height.

Try a question from the course

To choose a ratio, look at which two sides the question involves, measured from the angle you know. Say a ladder makes 65° with the ground, you know the ladder's length (the hypotenuse) and you want how high it reaches (the side opposite the angle). Opposite and hypotenuse means SOH, so use sine.

Now pick the ratio for a new triangle, then press Mark to check your answer in the course.

Who this course is for

• Students starting trigonometry, for example in geometry or an early high school or secondary maths course.
• Students revising SOH CAH TOA, the sine and cosine rules or radians before an exam such as GCSE Maths or the SAT.
• Physics and engineering students who need trig for resolving forces, waves and vectors.

What you need to know first

Basic algebra, especially rearranging a simple equation such as sin 30° = x/8, and Pythagoras' theorem. The Algebra course covers rearranging if it is new. You will want a scientific calculator for finding sides and angles.

How long it takes

There are 35 sections, and most take a few minutes: a short explanation with a slider or explorer, or a practice question with fresh numbers each time. Learners without a plan can open two sections of a course a day, in order, which takes 18 days. A plan removes the daily limit and lets you go straight to any topic, such as the cosine rule before a test.

Read next

Maths · TrigonometryUnit circle: chart, radians, sin, cos, tan and how to use itThe unit circle explained: a full chart in degrees and radians, how it gives sin, cos and tan, quadrant signs, reference angles and worked examples.