TRIGONOMETRY

Introduction

The word Trigonometry comes from two Greek words 'trigonon' and 'metron'. Trigonon means triangle and Metron means measurement. That is Trigonometry means measurement of triangles.

"Trigonometry is a branch of mathematics which deals with the measurement of triangles". 

The Greek astronomer Hipparchus is known as founder of Trigonometry. He developed trigonometry as a tool for his astronomical works. Ancient Indian mathematicians like Aryabhata, Bhaskara I, II and Brahmagupta were aware of many important results in Trigonometry. Thales (BC 600) is invariably associated with height and distance problems. Trigonometry has practical importance in navigation, seismology, designing electric circuits, surveying and simple harmonic motions in physics.

Pythagorean Theorem

         The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.?-500 B.C.?), who was perhaps the first to offer a proof of the theorem. But people had noticed the special relationship between the sides of a right triangle long before Pythagoras.

          

         The Pythagorean theorem states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypoteneuse, or, in mathematical terms, for the triangle shown at right, a² + b² = c². Integers that satisfy the conditions a² + b² = c² are called "Pythagorean triples." 
          We can't be sure if Pythagoras really was the first person to have found this relationship between the sides of right triangles, since no texts written by him were found. In fact, we can't even prove the guy lived. But the theorem a² + b²= c² got his name. Another Greek, Euclid, wrote about the theorem about 200 years later in his book called "Elements". There we also find the first known proof for the theorem. Now there are about 600 different proofs.

Today the Pythagorean theorem plays an important part in many fields of mathematics. For example, it is the basis of Trigonometry, and in its arithmetic form it connects Geometry and Algebra.

Angles

In geometry, an angle is defined as the inclination of two straight lines, which meet at a point. So in geometry an angle is always less than 360 degrees. But in Trigonometry, an angle is formed by rotating a revolving ray from one position to another. The initial position of the ray is called the initial side and the final position of the ray is called the terminal side.
The measure of an angle is the amount of rotation required to get to the terminal side from the initial side.

Measurement of Angles

In Trigonometry, angle is usually measured in degree and radian measures.
Degree measure : If the circumference of a circle is divided into 360 equal parts, then the angle subtended by a part at the center is called one degree. Each degree is divided into 60 equal parts, called minutes. Each minute is again subdivided into 60 equal parts called seconds.
In Trigonometry, an angle can be of any magnitude.
Radian measure : This is another unit of angle measurement. One radian is defined as the angle subtended at the center of a circle by an arc of length equal to the radius.