Trigonometry 1 (AQA GCSE Maths): Revision Notes

Trigonometry 1

What are trigonometric ratios?

Trigonometric ratios are mathematical relationships between the sides and angles in right-angled triangles. These ratios help us find missing angles when we know the lengths of two sides of a triangle.

The three trigonometric ratios

There are three main trigonometric ratios you need to know:

• Sine (sin): The ratio of the opposite side to the hypotenuse
• Cosine (cos): The ratio of the adjacent side to the hypotenuse
• Tangent (tan): The ratio of the opposite side to the adjacent side

Mathematical definitions

• $\sin x° = \frac{\text{opposite}}{\text{hypotenuse}}$
• $\cos x° = \frac{\text{adjacent}}{\text{hypotenuse}}$
• $\tan x° = \frac{\text{opposite}}{\text{adjacent}}$

How to label triangle sides

Before using trigonometric ratios, you must correctly identify the sides of your triangle:

1. Hypotenuse: Always the longest side, opposite the right angle
2. Adjacent: The side next to the angle you're working with (not the hypotenuse)
3. Opposite: The side across from the angle you're working with

The SOH CAH TOA memory aid

Finding missing angles using inverse functions

When you know two sides of a right-angled triangle and need to find an angle, you use inverse trigonometric functions.

What are inverse trigonometric functions?

Inverse trigonometric functions reverse the normal trigonometric operations:

• $\sin^{-1}$ (inverse sine)
• $\cos^{-1}$ (inverse cosine)
• $\tan^{-1}$ (inverse tangent)

Using your calculator

To find missing angles using trigonometry, follow this systematic approach:

1. Check your calculator is in degree mode - look for the 'D' symbol on the display
2. Identify which sides you know and which trigonometric function to use
3. Calculate the ratio of the two known sides
4. Use the appropriate inverse function ($\sin^{-1}$, $\cos^{-1}$, or $\tan^{-1}$)
5. Write down all figures from your calculator display, then round as required

Step-by-step method

Worked example approach

When solving trigonometry problems, it's important to understand the correct process:

Exam tips

When working with trigonometry in exams, remember these essential points:

• Always check your calculator is in degree mode before starting
• Show your working clearly by writing the trigonometric ratio you're using
• Round to the required accuracy - often 1 decimal place or 3 significant figures
• Label your triangle sides before choosing which trigonometric function to use