# Trigonometry

In trigonometry, we study about the right angled triangle, its angle formed with the base and the relation between its three sides. In maths Trigonometry is the study of the different relations which are formed between the different sides of the right angled triangle. In real life situations we come across certain situations, where we come across the right angled acute Triangles. If we look at a tall building at the top of it, then we find that the building forms a right angled triangle between the building and the flat surface of the earth. In such a situation, if we need to find the height of the building without actually measuring the height of the building. Let us take another example that you are sitting at the balcony of top floor of your house and the house is located over the bank of the river. If there exist a temple with a staircase at the bank of the river then if you look at the edge of the first stair case. If the height at which you are sitting is known and we know that a right angle is formed between the building and the river, then we can easily find the width of the river. This all is by the real life applications of the trigonometry in our life.

In these and many such situations we can find the distance and the height by using many real life mathematical techniques. We learn that word trigonometry is derived from the  Greek word “ tri”, which means three, “ gon “ means sides and word “menton “ stands for measure. Trigonometry is the study of the measure of the relationship between the three sides of the right angled triangle. If we talk about the study of some of the ratios of the sides of the right triangle with respect to the acute angles, then these types of ratios are called trigonometric ratios of the angles. Though these ratios are initially formed only for the acute angles, but they can be extended to other larger angles too. Let us take a right angled triangle, right angled at B, and angle CAB is an acute angle. So we say that AC is the Hypotenuse of the right triangle. The trigonometric ratios of the angle A in a right triangle ABC is defined as follows:
Sine of angle A = side opposite to angle A / Hypotenuse

= BC / AC

Cosine of angle A = side adjacent to angle A / Hypotenuse

= AB / AC

Tangent of angle A = side opposite to angle A / side adjacent to angle A

= BC / AB

Cosecant of angle A = 1 / Sine of angle A

= AC / BC

Secant of angle A = 1/ Cosine of angle A

= AC / AB

Cotangent of angle A = 1/ tangent of angle A

= AB / BC

The ratios we have discussed above are also called as   Sin A, Cos A, Tan A, Cosec A, Sec A and Cot A. The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the sides of the Triangles, if we find that the measures of the angles of the triangles remain same.

## Topics Covered in Trigonometry

• Trigonometric Functions

The functions of angles are known as trigonometric functions. They are also considered as circular functions. They are helpful in building the relationship of angles of triangle to length of sides of the triangle. Sine, cosine,...Read More

• Inverse Trigonometric Functions

In mathematics the inverse functions of the trigonometric function are known as inverse trigonometric functions. The functions such as arcsine, arc cos, arc tangent are the name of inverse trigonometric functions which ...Read More

• Introduction to Trigonometry
The branch of mathematics which studies the triangle and deals with relationship of angles and sides of the triangle is known as trigonometry. Trigonometry introduction defines the trigonometric functions and trigonometric iden...Read More
• Some Applications of Trigonometry
Trigonometry is the branch of mathematics which deals with triangles and relationship between the angles and sides of triangles is also defined by the trigonometry.
Now we will see some applications of trigonometry:
• Hyperbolic Trigonometry

In mathematics, hyperbolic functions are similar to trigonometric functions, and they can be defined in terms of exponential function. Here we will discuss hyperbolic trigonometry. We will also discuss hyperbolic functions iden...Read More

• What is Trigonometry

Trigonometry is a part of mathematics which deals with relationship between triangle and its sides. Trigonometry indicates the relationship between various elements of triangle. This is included in trigonometry definition....Read More

• Angles and their measurements
Angle can be defined as the union of two rays. These two rays have the same end point. In an angle one ray inclines over other ray that forms an angle. We represent an angle by the sign ∠.

Angle is that measure in mathematics which defines the direction of any object or mathematical shape or figure. We consider two units for it: degrees measure and radian measure. In degrees the angles can be written as 900, 450 a...Read More

• Unit Circle

Unit circle can be defined as a circle which has radius value 1. Now we will understand the process of making unit circle? Steps to follow to make a unit circle is shown below:

Step 1: To draw a unit circle we need to take radi...Read More

• Trigonometric Equations

Trigonometry equation can be defined as any equation which contains trigonometric functions. For example: Cos a = 1/ 2. If we have to calculate trigonometric equations using different functions then trigonometry equatio...Read More

• Applications of Trigonometry

Trigonometry is basically taught in schools under precalculus math. Before knowing the applications of trigonometry you should first understand the term trigonometry. Trigonometry is a branch of mathematics, it is ...Read More

• Trigonometric Identities

Trigonometry is a branch of mathematics which is used to show the relationship among the angles and sides of a triangle. In other word if we want to find relation between sides and angles of triangle then we will use t...Read More

• Graphs of Circular Functions

We know that graphing of any function is actually diagrammatic representation of that function. A function shows the relationship between two or more variables. There are six functions in trigonometry. These six fu...Read More

• Right Triangles Trigonometry

Right angle triangle can be defined as a triangle which contains a 90 degree angle. For right triangle one famous theorem defines the relationship between three sides, this theorem is Pythagoras theorem: