Know What Are the Trigonometry Formulas

Today, we will tell you in this article how to calculate the Trigonometric Formula if you don't know how to derive it. So, you can read this article. In this, we will explain all the Trigonometric Formulas, all the formulas of trigonometry, and we will also discuss the facts about it. So, read this article completely.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies the relationship between the sides and angles of triangles. Trigonometry is an integral part of geometry because every rectilinear figure can be resolved into triangles. In addition, trigonometry has complex relationships with other branches of mathematics, especially complex numbers, infinite series, differential calculus, and integration.

Trigonometry is actually derived from two Greek words, which are defined as follows:

Trigonon - Which means "three angles" (triangles).

Metron - Which means "measurement".

Types of Trigonometry

Trigonometry is used to measure the three sides of a triangle using trigonometric formulas. In a right-angled triangle, there are three sides: hypotenuse, perpendicular, and base.

The interpretation of any trigonometric formula is made from the following statement:

"In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle."

The sides of a right-angled triangle are defined as follows:

Hypotenuse: The side opposite the right angle (90°) is called the hypotenuse.

Perpendicular: The side that forms a 90° angle with the base is called the perpendicular.

Base: The remaining side of the right-angled triangle is called the base.

General Trigonometric Formulas

In mathematics, six functions of trigonometry are studied specifically, which help measure the sides and angles of triangles. After this, all the formulas are used in practice.

sinθ = perpendicular/hypotenuse = p/h

cosθ = base/hypotenuse = b/h

tanθ = perpendicular/base = p/b

cotθ = base/perpendicular = b/p

secθ = hypotenuse/base = h/b

cosecθ = hypotenuse/perpendicular = h/p

Table of Trigonometry formula

In trigonometry, there is more than one method for calculating the values of angles. But here only 0°, 30°, 45°, 60° and 90° are given for the purpose of remembering. We will study further the methods of proving trigonometry tables.

Symbol 0° 30° = π/6 45° = π/4 60° = π/3 90° =π/2

Sin θ 0 ½ 1/√2 √3/2 1

Cos θ 1 √3/2 1/√2 ½ 0

Tan θ 0 1/√3 1 √3 Undefined

Cot θ Undefined √3 1 1/√3 0

Sec θ 1 2/√3 √2 2 Undefined

Cosec θ Undefined 2 √2 2/√3 2/√3

Trigonometric Ratios of Angles

In the first quadrant i.e. the function of 90 changes into Sin – Cos, Tan – Cot and Cosec – Sec.

sin(90°−θ) = cos θ

cos(90°−θ) = sin θ

tan(90°−θ) = cot θ

cot(90°−θ) = tan θ

sec(90°−θ) = Cosec θ

Cosec(90°−θ) = sec θ

It is also expressed in the trigonometric formula as follows:

sin (π/2 – A) = cos A

cos (π/2 – A) = sin A

sin (π/2 + A) = cos A

cos (π/2 + A) = – sin A

sin (3π/2 – A) = – cos A

cos (3π/2 – A) = – sin A

sin (3π/2 + A) = – cos A

cos (3π/2 + A) = sin A

sin (π – A) = sin A

cos (π – A) = – cos A

sin (π + A) = – sin A

cos (π + A) = – cos A

sin (2π – A) = – sin A

cos (2π – A) = cos A

sin (2π + A) = sin A

cos (2π + A) = cos A

Trigonometric sum and difference of two angles

Sin(A+B) = Sin A . Cos B + Cos A . Sin B

Sin(A-B) = Sin A . Cos B − Cos A . Sin B

Cos (A+B) = Cos A . Cos B − Sin A . Sin B

Cos ( A-B ) = Cos A . Cos B + Sin A . Sin B

Tan ( A + B ) = (Tan A + Tan B) / ( 1 − Tan A . Tan B)

Cot ( A + B ) = (Cot A . Cot B − 1) / (Cot B + Cot A)

tan(A – B)= ( tan A – tan B )/ ( 1 + tan A . tan B )

cot(A – B) = (cot A . cot B + 1) / ( cot B – cot A )

Important Facts about Trigonometric Formulas

Trigonometry formulas are divided into two main categories in mathematics: trigonometric ratios and trigonometric identities. Trigonometric identities are a set of formulas that serve important functions in trigonometry.

Trigonometric ratios are used to determine the size of a triangle and the relationship between the lengths of its sides. There are many formulas in trigonometry, and all the necessary formulas are given above.

Conclusion

Through this article, we have learned about what Trigonometry is, all the Trigonometric Formulas, the sum and difference of trigonometric angles, and much more. We hope you found this article helpful.