Trigonometry 1 (Edexcel GCSE Maths): Revision Notes

Trigonometry 1

What are trigonometric ratios?

Trigonometric ratios are mathematical tools that help you find the size of an angle in a right-angled triangle when you know the lengths of two sides. These ratios create a relationship between the angles and sides of right-angled triangles.

To use trigonometric ratios effectively, you need to be able to identify and label the sides of a right-angled triangle correctly.

Labelling sides of a right-angled triangle

In any right-angled triangle, there are three sides that must be identified relative to the angle you're working with:

• Hypotenuse - This is always the longest side of the triangle, positioned opposite the right angle
• Adjacent - This is the side that touches the angle you're calculating (but isn't the hypotenuse)
• Opposite - This is the side that doesn't touch the angle you're calculating

Remember to label the hypotenuse first as it's always the same, then identify the adjacent and opposite sides based on the specific angle you're finding.

The three trigonometric ratios

There are three main trigonometric ratios you need to know:

Sine (sin)

$\sin x° = \frac{\text{opposite}}{\text{hypotenuse}}$

Cosine (cos)

$\cos x° = \frac{\text{adjacent}}{\text{hypotenuse}}$

Tangent (tan)

$\tan x° = \frac{\text{opposite}}{\text{adjacent}}$

Memory aid: SOH CAH TOA

Use SOH CAH TOA to remember these ratios:

Working through a trigonometry problem

Let's look at how to calculate an angle using trigonometric ratios step by step:

Using your calculator

To find a missing angle using trigonometry, you need to use inverse trigonometric functions:

• sin⁻¹ (inverse sine)
• cos⁻¹ (inverse cosine)
• tan⁻¹ (inverse tangent)

These are the reverse operations of sin, cos and tan.

For the example above, you would input: $\tan^{-1}\left(\frac{5}{6}\right) = 39.80557109°$