Trigonometry

The concept of trigonometry was introduced by the Greek mathematician Hipparchus, while the name trigonometry is a 16th century Latin derivative. Trigonometry is derived from the Greek word trigonon which means “triangle” and the word metron which means “measure” is a field of mathematics that analyses the links between triangle side lengths and angles. Applications of geometry to astronomical research gave rise to the field in the Hellenistic civilization during the 3rd century BC. The Greeks concentrated on chord calculations, whereas Indian mathematicians established the first tables of values for trigonometric ratios (also known as trigonometric functions) like sine.

Meaning of trigonometry

The principles of trigonometry encompass the measurement of angles as well as problems involving angles. Sine, cosine, and tangent are the three basic functions of trigonometry. These three basic ratios or functions can be used to construct other important trigonometric functions: cotangent, secant, and cosecant. All of the essential topics in trigonometry are built on the foundation of these functions. AS a result, in order to comprehend trigonometry, we must first study these functions and their formulas. 

The three sides of a right-angled triangle are as follows.

The side that is perpendicular to the angle ‘ A ’ is called perpendicular.

The neighbouring side of angle ‘ A ’ is called the base.

The hypotenuse is the side of the right angle that is opposite the right angle.

Using the formulas below and the above graphic, the six most essential trigonometric functions (trigonometric ratios) are determined. The sides of the right triangle are vital to understand since they define a set of important trigonometric functions. 

SinA = P / H

CosA = B / H

TanA = P / B

CosecA = H / P

SecA = H / B

CotA = B / P

Where P , B and H are the perpendicular, base and height of the right-angled triangle.

Trigonometric expressions 

In trigonometry, many formulas show the relationships between trigonometric ratios and angles for various quadrants. The following is a list of basic trigonometry formulas:

• Trigonometric ratios

SinA = P / H                             CosA = B / H

TanA = P / B                            CosecA = H / P

SecA = H / B                            CotA = B / P

Where P , B and H are the perpendicular , base and height of the right-angled triangle.

• Trigonometric formulas using Pythagoras’s identity

sin²A + cos²A = 1

1 + tan²A = sec²A or sec²A – tan²A = 1

1 + cot²A = cosec²A or cosec²A – cot²A = 1

• Trigonometry’s Sine and Cosine Law

a/sinB = b/sinB = c/sinC 

2ab cos C =  a² + b² – c²

2bc cos A =  b² + c² – a²

2ac cos B = a² + c² – b²

The lengths of the triangle’s sides are a, b, and c, and the triangle’s angle is A, B, and C.

Trigonometric tables 

The trigonometric table is made up of connected trigonometric ratios such as sine, cosine, tangent, cosecant, secant, and cotangent. In summary, these ratios are sin, cos, tan, cosec, sec, cot, and are used to calculate standard angle values. To learn more about these ratios, look at the trigonometric table chart.

Conclusion:

Trigonometry is one of the most important branches of mathematics that has a wide range of applications. The field of mathematics known as “trigonometry” studies the relationship between the sides and angles of a right-angle triangle. As a result, using trigonometric formulas, functions, or identities, it is possible to find the missing or unknown angles or sides of a right triangle. The angles in trigonometry can be measured in degrees or radians.

The ratios between the edges of a right triangle are known as trigonometric ratios. The following trigonometric functions of the known angle A, where a, b, and c correspond to the lengths of the sides, yield these ratios. 0⁰, 30⁰, 45⁰, 60⁰, and 90⁰ are some of the standard angles that are used in trigonometry. These angles’ trigonometric values can be found directly in the trigonometric table.