Edexcel GCSE Foundation Maths - What is Trigonometry?

Introduction

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It's used in many different fields, including engineering, architecture, and surveying.

The Basics

There are three main trigonometric ratios that you need to know:

• Sine (sin): Opposite side / Hypotenuse
• Cosine (cos): Adjacent side / Hypotenuse
• Tangent (tan): Opposite side / Adjacent side

SOH CAH TOA is a helpful mnemonic to remember these ratios:

• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent

Right-Angled Triangles

Trigonometry is mainly used with right-angled triangles. These triangles have one angle that measures 90 degrees.

Key terms:

• Hypotenuse: The side opposite the right angle (always the longest side).
• Opposite: The side opposite the angle you are interested in.
• Adjacent: The side next to the angle you are interested in (not the hypotenuse).

Using Trigonometry to Find Missing Sides and Angles

You can use the trigonometric ratios to find missing sides and angles in right-angled triangles. Here's how:

Finding a Missing Side:

1. Identify the angle you know.
2. Identify the sides you know and the side you want to find.
3. Choose the appropriate trigonometric ratio (SOH CAH TOA).
4. Set up an equation and solve for the unknown side.

Finding a Missing Angle:

1. Identify the sides you know.
2. Choose the appropriate trigonometric ratio (SOH CAH TOA).
3. Set up an equation and solve for the unknown angle using the inverse trigonometric functions (sin-1, cos-1, tan-1).

Example

Let's say we have a right-angled triangle with the following information:

• Angle A = 30 degrees
• Hypotenuse = 10 cm

We want to find the length of the opposite side.

1. Angle: We know angle A is 30 degrees.
2. Sides: We know the hypotenuse is 10 cm, and we want to find the opposite side.
3. Ratio: We need to use the sine ratio (SOH) because it involves the opposite and hypotenuse.
4. Equation: sin(30) = Opposite / Hypotenuse. Therefore, Opposite = sin(30) * Hypotenuse.
5. Solve: Opposite = sin(30) * 10 = 5 cm.

Practice

To get comfortable with trigonometry, practice solving various problems. You can find practice problems in textbooks, online resources, and past exam papers.

Key Tips:

• Label your sides clearly.
• Choose the correct trigonometric ratio.
• Use a calculator to find the sine, cosine, or tangent of an angle.
• Don't forget to use the inverse trigonometric functions to find angles.
• Check your answers and make sure they make sense in the context of the problem.

Conclusion

Trigonometry is an essential tool in mathematics and many real-world applications. By understanding the basics and practicing, you can confidently solve problems involving right-angled triangles.