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, cosine, tangent, cosecant, secant, and cotangent.

• Sine (sen or sin):

• Cosine (cos):

• Tangent (tg or tan):

• Cosecant (cosec or csc):

• Secant (sec):

• Cotangent (cot):

Fundamental Trigonometric Identity

The most important relationship among the trigonometric functions is the Pythagorean identity:

• Pythagorean Identity:

Sum and Difference Formulas

These formulas allow the calculation of the sine, cosine, or tangent of the sum or difference of two angles.

• Cosine of Sum:

• Cosine of Difference:

• Tangent of Sum: Additional info: Formula inferred for completeness.

• Tangent of Difference: Additional info: Formula inferred for completeness.

Double Angle Formulas

Double angle formulas express trigonometric functions of in terms of .

• Sine Double Angle:

• Cosine Double Angle:

• Tangent Double Angle: Additional info: Formula inferred for completeness.

Reciprocal and Quotient Identities

These identities relate the trigonometric functions to each other through reciprocals and quotients.

Table: Trigonometric Functions and Their Relationships

Example: Using the Double Angle Formula

• Problem: Find if and is in the first quadrant.

• Solution: First, find using the Pythagorean identity: .

• Now, .