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’:

Основные тригонометрические тождества

and

the Fundamental trigonometric identity

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

Основные тригонометрические тождества

 

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

 

Основные тригонометрические тождества

Tangent and Cotangent Identities. Relations Between Tangent and Cotangent

 

Основные тригонометрические тождества

Tangent and Cotangent Identities. Relations Between Trigonometric Functions

 

Основные тригонометрические тождества

and

 

Основные тригонометрические тождества

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

 

Основные тригонометрические тождества