Trigonometry includes a vast syllabus different kinds of problems are solved using various formulas of trigonometry. There are various ratios of trigonometry such as sin, cosec, cot, sec, cos, tan which help to solve the problems. Also, it has identities like Pythagorean, etc. It is that branch of maths that deals with various triangles. Trigonometry is recognized as the learning of relations amongst lengths and angles of numerous triangles as well. The uses of the formula that are included in trigonometry, are not only important in mathematics but other subjects as well. Like the study of geography uses the methods of triangulation for measuring the distances between different given landmarks. It is widely used in navigation systems in satellites, trigonometry also finds a place in Astronomy for studying the measurements to reach the stars that are nearby.
Trigonometry is a very interesting topic, learning to solve problems by using various formulas and trigonometry table in this particular topic helps you score well in your exams. Some of the important formulas like ratio signs in various quadrants including shifting angles, identities of differences and sums, identities that have single and double angles, etc. are really important to understand.
When you learn about the trigonometry formulas, you consider them for right-angled triangles only. In a triangle, there are three sides – Hypotenuse, Opposite side, and Adjacent side. The side which is the longest is called the hypotenuse, the opposite side of the angle is perpendicular, hypotenuse and opposite side rest on the adjacent side.
Trigonometry has lots of formulas, here is the list.
- Basic trigonometry formulas
- Inverse formulas for trigonometry
- Sum of the identities of product
- Identities of product
- Identities that have a half angle
- Identities that have a triple angle
- Periodic identities
- Identities that have Co- function
- Identities of difference and sum
- Identities that have a double angle
- Reciprocal identities
- Table of trigonometry
Basic function formulas for trigonometry
There are essentially six ratios that are used to find the fundamentals of Trigonometry. These are known as functions of trigonometry. The six functions are cosine, co-tangent, tangent, co-secant, secant, and sine.
For reference, we use a right-angled triangle, and the functions and trigonometric identities are used for deriving:
- sin θ = hypotenuse or Opposite Side
- cot θ = Adjacent Side or Opposite Side
- tan θ = Opposite Side or Adjacent Side
- sec θ = Hypotenuse or Adjacent Side
- cosec θ = Hypotenuse or Opposite Side
- cos θ = hypotenuse or Adjacent Side
Two Major Systems in which the trigonometric formulas are divided are:
- Trigonometric Identities: These formulas involve the functions of trigonometry. For all the standards of the variable quantity, these identities hold true. These formulas are vital for solving all kinds of applications of trigonometry. The formulas are derived with the help of these identities, which help in solving the problems. These formulas also help to determine the domain, array, value, and range of a compound of trigonometry function
- Trigonometric Ratios: These are known for the association amongst the measurement of angles and the length of the right triangle of its sides.
The identities that are reciprocal, also play an important role in trigonometry and they are given as:
- cosec θ = 1/sin θ
- tan θ = 1/cot θ
- cos θ = 1/sec θ
- sin θ = 1/cosec θ
- cot θ = 1/tan θ
- sec θ = 1/cos θ
You take all of these from the right-angled triangle. When you know the values of the height and base of a right-angled triangle, it becomes easy to find out the sine, cotangent, cosecant, secant, tangent, and cosine values using the formulas for trigonometry. The trigonometric identities that are reciprocal are also calculated by making use of the functions of trigonometry.
Trigonometry has lots of formulas to learn and practice. Cuemath provides expert advice on the same. You just have to refer them for any doubt and you are sorted. Wishing you the very best for preparing this interesting chapter.