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Understanding Trigonometry in Mathematics.

Published on Aug 18, 2025 • Education

Introduction

Hi guys, welcome to today’s tutorial. In this class, we’ll be exploring the fundamentals of Trigonometry. After the lesson, there will be practical questions for you to attempt, so make sure you stick around. If you haven’t subscribed yet, do so now to stay updated with more tutorials.

Let’s get started with the questions and answers.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies the relationship between the angles and sides of a triangle, especially right-angled triangles.

While we have different types of triangles such as:

• Scalene triangle
• Equilateral triangle
• Isosceles triangle

Trigonometry primarily focuses on the right-angled triangle.

Right-Angled Triangle

A right-angled triangle is a triangle that has one angle equal to 90°.

• If a triangle has an angle of 90°, it qualifies as a right-angled triangle.
• This type of triangle forms the foundation for basic trigonometric ratios.

Naming the Sides of a Right-Angled Triangle

In a right-angled triangle, the sides are classified based on their positions relative to the known angle (apart from the right angle).

1. Opposite Side
   • This is the side facing the chosen known angle.
   • Example: If angle X is the known angle, the side directly opposite X is the opposite.
2. Adjacent Side
   • This is the side beside the known angle, excluding the hypotenuse.
   • It is the side that forms the angle together with the right angle.
3. Hypotenuse
   • This is the side directly facing the 90° angle.
   • It is always the longest side of a right-angled triangle.

Watch the full tutorial here: https://www.youtube.com/watch?v=wKCP6MQiTac

Why These Definitions Matter

The correct identification of opposite, adjacent, and hypotenuse is what gives rise to the basic trigonometric ratios:

• Sine (sin⁡) = Opposite ÷ Hypotenuse
• Cosine (cos⁡) = Adjacent ÷ Hypotenuse
• Tangent (tan⁡) = Opposite ÷ Adjacent

These ratios are the building blocks of trigonometry and appear frequently in JUPEB, WAEC, NECO, NABTEB, and JAMB mathematics exams.

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Keywords.

• Trigonometry basics explained
• Definition of trigonometry
• Right-angled triangle in mathematics
• Opposite, adjacent, and hypotenuse meaning
• Sine, Cosine, and Tangent explained
• JUPEB Mathematics past questions
• WAEC/NECO trigonometry tutorial
• Step-by-step trigonometry notes