Basic Trigonometric Ratios

There are 6 ratios in trigonometry. These are referred to as Trigonometric Functions. Below is the list of trigonometric ratios, including sine, cosine, secant, cosecant, tangent and cotangent.

List of Trigonometric Ratios
Trigonometric Ratio	Definition
sin θ	Perpendicular / Hypotenuse
cos θ	Base / Hypotenuse
tan θ	Perpendicular / Base
sec θ	Hypotenuse / Base
cosec θ	Hypotenuse / Perpendicular
cot θ	Base / Perpendicular

Unit Circle Formula in Trigonometry

For a unit circle, for which the radius is equal to 1, θ is the angle. The values of the hypotenuse and base are equal to the radius of the unit circle.

Hypotenuse = Adjacent Side (Base) = 1

The ratios of trigonometry are given by:

sin θ = y/1 = y
cos θ = x/1 = x
tan θ = y/x
cot θ = x/y
sec θ = 1/x
cosec θ = 1/y

Trigonometric Functions Diagram

Trigonometry Formulas – List of All Trigonometric Identities and Formulas

Trigonometry formulas are equations that relate the sides and angles of triangles. They are essential for solving a wide range of problems in mathematics, physics, engineering and other fields.

Here are some of the most common types of trigonometry formulas:

Basic definitions: These formulas define the trigonometric ratios (sine, cosine, tangent, etc.) in terms of the sides of a right triangle.
Pythagorean theorem: This theorem relates the lengths of the sides in a right triangle.
Angle relationships: These formulas relate the trigonometric ratios of different angles, such as sum and difference formulas, double angle formulas, and half angle formulas.
Reciprocal identities: These formulas express one trigonometric ratio in terms of another, such as sin(θ) = 1/coc(θ).
Unit circle: The unit circle is a graphical representation of the trigonometric ratios, and it can be used to derive many other formulas.
Law of sines and law of cosines: These laws relate the sides and angles of any triangle, not just right triangles.

Read on to learn about different trigonometric formulas and identities, solved examples, and practice problems.

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