# Trigonometry

**What is Trigonometry?**

Trigonometry is a branch of mathematics focused on measuring the angles and sides of triangles using given information.

The word "trigonometry" comes from the Greek words "*trigonos*" (meaning triangle) and "*métron*" (meaning measure).

So, the meaning is quite straightforward: it’s the study of measuring triangles.

**The History of Trigonometry**

The origins of trigonometry are credited to the ancient Greeks, although early concepts can also be found in ancient Egypt and Mesopotamia.

Traditionally, **Hipparchus of Nicaea**, a Greek astronomer from Alexandria in the 2nd century BC, is regarded as the father of trigonometry. He was one of the first to study the lengths of chords in a unit circle.

The Greeks applied trigonometry extensively in their astronomical works, with one of the most notable being the **Almagest**, written by Ptolemy in the 2nd century AD.

During the Middle Ages, Greek trigonometric texts were translated into Arabic, and in the 15th century, these Arabic versions were translated into Latin, bringing trigonometry to Europe.

**Trigonometry Resources**

**Trigonometry**

- Trigonometry
- The unit circle
- Angle
- Oriented angle
- Degree measure
- Sexagesimal degree
- How to sum two angles in degrees, minutes, seconds
- Radians
- How to convert degrees and radians
- How to measure an arc of a circle
- How to calculate the area of a circular sector
- Trigonometric functions

**Trigonometry**

- Trigonometric functions
- Sine
- Cosine
- Tangent
- Cotangent
- Arcsine
- Arccosine
- Arctangent
- Arccotangent
- Secant
- Cosecant
- Sinusoidal functions
- The first fundamental trigonometric identity
- The second fundamental trigonometric identity
- The relationship between tangent and the slope of a line
- Trigonometric values of 30° or π/6
- Trigonometric values of 45° or π/4
- Trigonometric values of 60° or π/3
- Associated angles
- Reduction to the first quadrant
- Addition and subtraction formulas
- Cosine subtraction
- Cosine addition
- Sine addition
- Sine subtraction
- Tangent addition
- Tangent subtraction
- Phase angle
- How to calculate the angle between two lines
- Relationship between the slopes of perpendicular lines
- Double angle formulas
- Half angle formulas
- Parametric formulas
- Prosthaphaeresis formulas
- Werner formulas

**Trigonometric equations**

- Trigonometric equations
- Basic trigonometric equations
- How to transform a trigonometric equation into a basic form
- Linear trigonometric equations in sine and cosine
- The geometric method for solving linear trigonometric equations in sine and cosine
- The added angle method for solving linear trigonometric equations in sine and cosine
- Second-degree trigonometric equations in sine and cosine (homogeneous and non-homogeneous)
- Systems of trigonometric equations
- Trigonometric inequalities
- Systems of trigonometric inequalities
- Parametric trigonometric equations

**Right triangle**

- The first theorem of the right triangle
- The second theorem of the right triangle
- How to solve the right triangle using trigonometry

**Applications**

- The area of a triangle using trigonometry
- The chord theorem
- The radius of a circumcircle around a triangle
- The sine theorem
- The cosine theorem
- How to solve the triangle using trigonometry
- Sine of a matrix
- Cosine of a matrix