Trigonometric Identities and Functions

Basic Trigonometric Functions

Trigonometric functions relate the angles of a triangle to the lengths of its sides. The six primary trigonometric functions are:

• Sine (sen or sin):

• Cosine (cos):

• Tangent (tg or tan):

• Cotangent (cot):

• Secant (sec):

• Cosecant (cosec or csc):

Fundamental Trigonometric Identity

The most important identity in trigonometry, known as the Pythagorean Identity, is:

This identity is fundamental for deriving other trigonometric relationships.

Sum and Difference Formulas

These formulas allow the calculation of the sine and cosine of sums or differences of two angles:

• Cosine of Sum:

• Cosine of Difference:

• Tangent of Sum:

Example: To find , use and apply the sum formula.

Double Angle Formulas

Double angle formulas express trigonometric functions of in terms of :

• Sine Double Angle:

• Cosine Double Angle:

• Tangent Double Angle:

Example: If and is in the first quadrant, find using the double angle formula.

Reciprocal and Quotient Identities

These identities relate the trigonometric functions to each other:

Table: Trigonometric Functions and Their Relationships

Additional info:

• Some terms are written in Portuguese (e.g., "sen" for sine, "cosseno" for cosine, "cotagente" for cotangent, "secante" for secant, "cossecante" for cosecant, "tg" for tangent).

• Formulas and relationships are standard in trigonometry and are essential for solving equations and simplifying expressions.