Trigonometric Ratios

Definition

Trigonometric ratios are the ratios of the sides of a right-angled triangle. The six trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent, denoted as sin, cos, tan, csc, sec, and cot respectively.

Basic Trigonometric Ratios

For a right-angled triangle with sides a, b, and hypotenuse c, and an angle θ:

• Sine (sin θ) = Opposite/Hypotenuse = a/c
• Cosine (cos θ) = Adjacent/Hypotenuse = b/c
• Tangent (tan θ) = Opposite/Adjacent = a/b

Reciprocal Trigonometric Ratios

The reciprocal trigonometric ratios are the reciprocals of the basic ratios:

• Cosecant (csc θ) = 1/Sine = c/a
• Secant (sec θ) = 1/Cosine = c/b
• Cotangent (cot θ) = 1/Tangent = b/a

Study Guide

To study trigonometric ratios, follow these steps:

1. Understand the basic definitions and concepts of right-angled triangles and angles.
2. Memorize the trigonometric ratios and their definitions.
3. Practice solving problems involving trigonometric ratios, such as finding missing sides or angles in a right-angled triangle.
4. Learn about the unit circle and how it relates to trigonometric ratios.
5. Understand the application of trigonometric ratios in real-life situations, such as navigation, engineering, and physics.

Remember to practice regularly and seek help if you encounter difficulties in understanding any concept related to trigonometric ratios.