An Introduction to Trigonometry (Mathematics Lesson)

What Is Trigonometry?

Trigonometry is about triangles. In particular, it is about right angled triangles.

Trigonometry relates the lengths of the sides of the triangle with the angles.

What Are the Sides and Angles of a Right Angled Triangle?

The sides and angles of a right angled triangled are shown below:

The right angle is shown by the little square in the corner of the triangle.

An angle is shown by the curved line, and is labelled θ (the Greek letter theta).

The longest side is called the hypotenuse.

The side opposite the angle θ is called the opposite.

The side adjacent (next) to the angle θ is called the adjacent.

The Sine, Cosine and Tangent Functions

The sine, cosine and tangent fuctions (often shortened to sin, cos and tan) show how the sides and angles are related to each other.

The sine, cosine and tangent of the angle θ are related to ratios of two of the sides of the right angled triangle:


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The word trigonometry comes from two ancient Greek words:

trigonon 'triangle' + metron 'measure'


A useful way of remembering the equations is SOH CAH TOA.

SOH stands for Sine equals Opposite over Hypotenuse.

CAH stands for Cosine equals Adjacent over Hypotenuse.

TOA stands for Tangent equals Opposite over Adjacent.

SOH CAH TOA can be remembered phonetically - it sounds like 'Sockatoa'.

There are also useful mnemonics to remember it:

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  • Stamp Out Homework Carefully As Having Teachers Omit Assignments

  • Some Old Horse Caught Another Hourse Taking Oats Away

  • Some Old Hag Cracked All Her Teeth On Asparagus
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