Fundamental Trigonometric Identities. Formulas

 

The Fundamental trigonometric identities represent mathematical expressions for trigonometric functions that are valid for all values of the argument (from the common domain of trig functions).

Fundamental trigonometric identities typically include the following expressions:

 

The Fundamental trigonometric identity is called the ‘Pythagorean trigonometric identity’:

and

We can use the Pythagorean identity to solve for sin α or cos α:

 

We can use the Pythagorean identity to solve for tan α or cot α:

 

Tangent and Cotangent Identities. Relations Between Tangent and Cotangent

 

Tangent and Cotangent Identities. Relations Between Trigonometric Functions

 

and

 

In a right triangle, the sine of one acute angle equals the cosine of the other acute angle

 

Similar topics

 

Proof of the Pythagorean Identity for Sine and Cosine

Proof of the Pythagorean Identities for Tangent and Cotangent

Why the Fundamental trigonometric identity is called the ‘Pythagorean trigonometric identity’

How to use the Pythagorean identity

Proof of Relations Between Trigonometric Functions (tan, cot, sin and cos)

Proof of Relationship between the Tangent and Cotangent

Theorem of the equality of the sine and cosine of different angles