"GCSE Maths Revision: Unlocking the Secrets of Pythagoras and Trigonometry...

Understanding Pythagoras' Theorem

Pythagoras' Theorem is a fundamental principle in geometry, essential for solving problems involving right-angled triangles. It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

• Formula: a2 + b2 = c2
• Applications: Used to find the length of a side in a right-angled triangle when the other two sides are known.

Example Problem

Given a right-angled triangle with sides a = 3 and b = 4, find the hypotenuse c.

Solution: 32 + 42 = c2 9 + 16 = c2 c = 5

Exploring Trigonometry

Trigonometry deals with the relationships between the angles and sides of triangles. It is crucial for solving problems involving non-right-angled triangles and for understanding wave patterns, among other applications.

Key Trigonometric Ratios

• Sine (sin): Opposite side over hypotenuse
• Cosine (cos): Adjacent side over hypotenuse
• Tangent (tan): Opposite side over adjacent side

Using Trigonometric Ratios

These ratios are used to calculate unknown angles and sides in right-angled triangles. For example, to find an angle θ:

If sin θ = 0.5, then θ = 30° (using a calculator or trigonometric tables).

Tips for Exam Success

1. Practice Regularly: Consistent practice helps reinforce concepts and improve problem-solving speed.
2. Understand Concepts: Focus on understanding the 'why' behind formulas and theorems.
3. Use Past Papers: Familiarize yourself with exam formats and question types by solving past papers.

For more resources and practice questions, consider visiting educational websites or consulting your textbook.