Introduction to Trigonometry

Sine, cosine, and tangent are just ratios in a right triangle

Trigonometry sounds intimidating, but it's built on one simple idea: in a right triangle, the ratios between the sides are always the same for a given angle. These ratios have names — sine, cosine, and tangent.

The classic memory trick is SOH-CAH-TOA: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.

In this lesson, you'll see a right triangle on the graph with labeled sides. The AI tutor will walk you through each ratio step by step — and show you why these ratios are so useful.

Related Topics

Pythagorean TheoremThe Unit CircleSine & Cosine

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What is SOH-CAH-TOA?
SOH-CAH-TOA is a memory trick: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent. These are the three basic trig ratios in a right triangle.
What do opposite, adjacent, and hypotenuse mean?
In a right triangle, pick an angle (not the right angle). The side across from it is the opposite. The side next to it (not the hypotenuse) is the adjacent. The hypotenuse is always the longest side, opposite the right angle.
What is sine of an angle?
Sine of an angle = opposite side ÷ hypotenuse. For a 3-4-5 triangle with a 53° angle, sin(53°) = 4/5 = 0.8. It tells you what fraction of the hypotenuse the opposite side is.
Why is trigonometry useful?
Trigonometry lets you find missing sides and angles in triangles. It's used in architecture, navigation, physics, engineering, computer graphics, and anywhere you work with angles and distances.
What can it graph?
It can plot explicit, implicit, and parametric functions, add points and geometry, and animate sliders on the same graph.
Can I use voice or a photo?
Yes. You can talk to the tutor, upload a worksheet or handwritten problem, and let the graph update from that input.
Will it explain the steps?
Yes. The AI explains what it is drawing and why, so you see the answer on the graph instead of getting only a final number.