learn to me trigonometry

Welcome! I'm thrilled to help you master trigonometry. It's one of the most practical and beautiful branches of math, linking the angles of a triangle directly to the lengths of its sides.

Before we dive into the math, I'd love to know a little bit about your goals and what you've studied before so we can tailor this perfectly to you.

What is your main goal for learning trigonometry, and how much prior math background do you have with basic geometry or algebra?

teach me trigonometry

Let's kick things off by getting standard on the absolute basics: the anatomy of a right triangle.

In trigonometry, everything starts with a right triangle (a triangle where one angle is exactly 90 degrees). To make sense of the math, we name the three sides based on their relationship to a specific angle, which mathematicians usually call (written as the Greek letter

\theta

Here are the three labels we use:

Hypotenuse: This is the absolute longest side of the right triangle. It is always directly across from the 90-degree right angle itself, and its position never changes.
Opposite: This is the side directly across from our chosen angle $\theta$ . If you stood at the corner of angle $\theta$ and looked straight ahead, you would be staring right at this side.
Adjacent: This means "next to". It is the side that helps form the angle $\theta$ but is not the hypotenuse.

A right-angled triangle with side labels relative to an acute angle theta.

I have created an interactive visualization above. Try clicking the different angles to see how the 'Opposite' and 'Adjacent' sides swap places depending on where you are looking from, while the 'Hypotenuse' stays completely fixed.

Once you feel comfortable telling those three sides apart, we can look at how we turn them into the famous ratios: Sine, Cosine, and Tangent.