Introduction to Trigonometric Ratios

Trigonometric ratios are mathematical expressions that relate the angles and sides of a right-angled triangle. These ratios are used to solve problems involving right-angled triangles and are fundamental in the field of trigonometry.

Basic Trigonometric Ratios

There are three primary trigonometric ratios, which are defined as follows:

Sine (sin) Ratio: The sine of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos) Ratio: The cosine of an angle in a right-angled triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan) Ratio: The tangent of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

How to Use Trigonometric Ratios

To use trigonometric ratios, you need to identify the angle or sides you are working with in the right-angled triangle. Then, you can use the appropriate trigonometric ratio to calculate the unknown angle or side.

Study Guide

To effectively study and understand trigonometric ratios, follow these steps:

Understand the definitions of sine, cosine, and tangent ratios.
Learn to identify the opposite, adjacent, and hypotenuse sides in a right-angled triangle.
Practice applying the trigonometric ratios to solve real-world and mathematical problems.
Memorize the mnemonic "SOHCAHTOA" to remember the relationships between sine, cosine, and tangent ratios.
Review and practice using trigonometric ratios in various contexts to reinforce your understanding.