Trigonometry Fundamentals

This page introduces essential concepts in trigonometry, focusing on the relationships between angles and sides in right-angled triangles. It covers Pythagoras' theorem and trigonometric ratios, providing a solid foundation for understanding trigonometric ratios for beginners.

The page begins by presenting Pythagoras' theorem, a fundamental principle in trigonometry. The theorem is expressed as a²+ b² = c², where c represents the hypotenuse of a right-angled triangle. This formula is crucial for calculating unknown side lengths in right-angled triangles.

Definition: Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

The document then introduces the concept of trigonometric ratios, which are relationships between the sides of a right-angled triangle. These ratios are typically represented using Greek letters, with θ (theta) commonly used to denote angles.

Vocabulary: The sides of a right-angled triangle are labeled as:

• Adjacent: The side next to the angle of interest
• Opposite: The side across from the angle of interest
• Hypotenuse: The longest side, opposite the right angle

The page explains the three main trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). These ratios are defined in terms of the sides of a right-angled triangle:

Highlight: The trigonometric ratios are:

• Sin θ = opposite / hypotenuse
• Cos θ = adjacent / hypotenuse
• Tan θ = opposite / adjacent

To help students remember these ratios, the mnemonic SOHCAHTOA is introduced. This memory aid is widely used in trigonometry GCSE worksheets and revision materials.

Example: In a right-angled triangle ABC with the right angle at C, if angle B is the angle of interest:

• Sin B = AC / AB (opposite / hypotenuse)
• Cos B = BC / AB (adjacent / hypotenuse)
• Tan B = AC / BC (opposite / adjacent)

This comprehensive overview provides students with the essential knowledge needed for solving trigonometric problems and understanding more advanced concepts in trigonometry. The clear explanations and visual representations make this an excellent resource for trigonometry revision pdf materials and GCSE trigonometry worksheets.