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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.

Graph

FAQ

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.

Related Topics

Pythagorean TheoremThe Unit CircleSine & Cosine