Trigonometry for GCSE Maths: Explanation, Examples and Questions

Trigonometry is a key topic in GCSE and iGCSE maths, helping students understand the relationships between angles and sides in triangles.

At GCSE level, you’ll cover basic trigonometry (finding missing angles and sides), trigonometry in 3D, graphing trigonometric functions, and solving trigonometric equations using sine, cosine, and tangent.

These skills are essential for tackling more advanced maths topics and real-world applications in fields like physics, engineering, and architecture.

Basic Trigonometry

If you've heard of SOH CAH TOA before but have no idea what that means then start here!

This video is a good introduction to trigonometric functions, what they are, and how to use them in order to find missing sides and missing angles of right angled triangles.

3D Trigonometry

When you feel confident with the basics of trig, watch this video on how to use trigonometry to find missing sides and angles in 3D objects such as cuboids, triangular prisms, and pyramids.

Graphs of Sin, Cos and Tan

Being able to sketch the graphs of trig functions can help us to solve trigonometric equations which often have 2 solutions between 0° and 360°.

You can also be asked in your exam to sketch the graphs of sine, cosine or tangent.

Exact Trig Values

The mathematics syllabus requires that students know the exact values of sine and cosine for angles 0°, 30°, 45°, 60° and 90° and the exact values of tangent for angles 0°, 30°, 45°, and 60°.

This is especially required for non-calculator papers where you could be asked for the value of sin 30° without the use of a calculator.

Although this might sound daunting, it's not necessary to memorise every single angle!

We can use knowledge of special triangles plus the graphs of sine, cosine and tangent in order to work out the exact values of sin, cos, and tan without memeorising them all!

Solving Trig Equations

Solving trig equations usually involves rearranging a one or two step equation and then using inverse trigonometric functions to find a missing angle.

As there are usually two solutions, you will also need to find the second solution. A sketch of a graph can help you with this.

The Sine Rule, Cosine Rule, and Area of Any Circle

These three videos show how to use the sine and cosine rules to find the missing side lengths of any triangles - not just right angled triangles.

The area of a right angled triangle can be found by ½ × base × height but the area of any triangle can be found using the formula area = ½ ab sin C.

The rest of the lesson on trigonometry is not quite ready, but if you already know what you're doing, we have practice questions linked below.