Trigonometry

What is Trigonometry?

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

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

 

 
 

Please feel free to point out any errors or typos, or share suggestions to improve these notes. English isn't my first language, so if you notice any mistakes, let me know, and I'll be sure to fix them.

Trigonometry

Trigonometry

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

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
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Trigonometry

Trigonometric Laws and Formulas

Hyperbolic Functions

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