Understanding Trigonometric Functions and Solving Problems

This page provides a comprehensive introduction to trigonometry, focusing on the fundamental concepts and problem-solving techniques for right-angled triangles. It covers the identification of sides, trigonometric ratios, and practical applications of these principles.

The page begins by defining the sides of a right-angled triangle:

Definition: In a right-angled triangle, the side opposite the right angle is called the hypotenuse and is always the longest side. The side opposite to the angle in question is called the opposite side, and the remaining side is called the adjacent side.

The trigonometric ratios are then introduced:

Highlight: The main trigonometric ratios are:

• Sine (sin) = opposite / hypotenuse
• Cosine (cos) = adjacent / hypotenuse
• Tangent (tan) = opposite / adjacent

These ratios are often remembered using the mnemonic SOH-CAH-TOA.

The page provides several examples of how to solve trigonometric problems step by step for beginners. One such example demonstrates finding an angle using the cosine function:

Example: Given a triangle with a hypotenuse of 13cm and an adjacent side of 11cm, to find angle x:

1. Identify the known sides and the ratio to use (cos x = adjacent / hypotenuse)
2. Substitute the values: cos x = 11 / 13
3. Take the inverse cosine (arccos or cos^-1) of both sides
4. Calculate: x = cos^-1(11/13) ≈ 32.2°

The page also includes examples of how to solve trigonometric equations with sin and cos, demonstrating how to find missing sides in a triangle using these functions.

Highlight: When solving for a missing side, always ensure you're using the correct trigonometric ratio based on the given information and what you're trying to find.

The transcript concludes with a table of common angle values for sin, cos, tan functions, which is useful for quick calculations and understanding the behavior of these functions:

Example: Some common angle values include:

• sin 30° = 1/2
• cos 30° = √3/2
• tan 30° = 1/√3
• sin 45° = cos 45° = 1/√2
• tan 45° = 1

This information provides a solid foundation for understanding trigonometric functions with examples and offers a practical guide for solving trigonometric equations step by step.