Trigonometry: Learning These Formulas Is Mandatory!


Last Updated on January 20, 2024 by Asfa Rasheed

Trigonometry is the mathematical discipline that studies angles’ functions and their use via Trigonometry Formulas, laws, and identities. Trigonometric identity is used in architecture, stringed instruments, engineering and a variety of other specialisations in science. 

Students in trigonometry have to work out proportions of sides of the triangle to calculate the measurement of an angle. The most fundamental trigonometric terms comprise sine as well as cosine. Every trigonometry equation requires students to know the various relationships that involve cosine, secant, sine, tangent and cotangent.

Through studying the trigonometry formulas, students will also learn about the subject of Pythagorean identities products, identities for products and angles that are negative, radians, triple angle formulas, and much more. 

Find out more here for an inventory of trigonometry equations as well as other related concepts.

List of Trigonometry Formulas

After knowing the basics of trigonometry, let’s now understand that these are divided into various categories by the trigonometry terms associated with them. Let’s take a look at the following sets of trigonometry formulas in various categories.

  • Fundamental Trig Ratio Formulas: These are trigonometry formulas that relate to the fundamental trigonometric proportions of cos, sin, tan, and so on.
  • Reciprocal Identities: This is a reference to trigonometry formulas addressing the reciprocal relationship between trigonometry ratios.
  • Trigonometric Ratio Table: Trigonometry values are illustrated for normal angles within the table of trigonometry.
  • Periodic Identities: These are trigonometry equations that aid in determining the values of trigonometry functions to determine a change in angles due to 2p, p/2 and more.
  • Co-function identities: Trigonometry formulas for cofunction identities illustrate interrelations among the trigonometric functions.
  • Identification of Sum or Difference: These trigonometry formulas are utilised to calculate the trigonometric formula for the sum or difference of angles.
  • Double, Triple, and Half Identities: These formulas contain the trig function values for half, double, or triple angles.
  • Sum to Product Identities: These trigonometry formulas can be used to show the trigonometric function’s product in terms of their sum or vice versa.
  • Inverse Trigonometry Formulas: The formulas for inverse trigonometry include the formulas related to inverse trig functions such as sine reverse, cosine inverse etc.
  • Sine Law and Cosine Law

Trigonometry Formula List

Trigonometry is a branch of maths that is concerned primarily with triangles. It’s also known for studying the relationship between the angles and lengths of trigonometric triangles. When we learn about trigonometric formulas, it is essential to think about only triangles with right angles. However, they apply to other triangles too.

In a right-angled triangular, you will find three edges: the hypotenuse side to the left (perpendicular) and the adjacent side (base). 

The longest of the sides is known as the hypotenuse. The opposite side of the angle is known as the perpendicular side and the side on which both the hypotenuse and the opposite side are located in the side adjacent to it.

Different sets of formulas for trigonometry are listed here:

  • Basic Formulas
  • Trigonometric Ratio Table
  • Reciprocal Identities
  • Periodic Identities
  • Cofunction Identities
  • Half-Angle Identities
  • Sum and Difference of Identities
  • Double Angle Identities
  • Product Identities
  • Sum of Product Identities
  • Triple Angle Identities
  • Sine Law and Cosine Law
  • Inverse Trigonometry Formulas

Trigonometry Formulas

Undoubtedly, Trigibinetry formulas are not that easy. While you can memorise these, you need to be diligent towards regular revisions. 

Six fundamental trigonometric ratios are used in this formulas. They are referred to as trigonometric functions and utilize all trigonometry equations. 

The basic trigonometric terms include secant, cosecant, sine, cosine and cotangent. The trigonometric identities and functions are calculated, making use of the right-angled triangular. 

When the height and bottom side of the right-angled triangle are identified, we can determine the cosine, tangent, secant, sine, cosine, cosecant and cotangent values using trigonometric formulas.

Basic Trigonometric Formulas

Following are the basic Trigonometric formulas, and ensure you remember all of these very well. These formulas form the basis of any calculation in trigonometry, implying the need to understand the differences between each and how to apply them correctly.

Formulas That Involve Reciprocal Identities

Cosecant and secant, and cotangent refer to the mutual inverses of the three basic trigonometric ratios sine, cosine, and tangent. All the reciprocal identities can also be derived by using a right-angled triangular figure as an example. 

These trigonometric reciprocal identities are created using trigonometric formulas. The trigonometry formulas based on reciprocal identities are often used to make trigonometric calculations simpler.

  • sec θ = 1/cos θ
  • cosec θ = 1/sin θ
  • cot θ = 1/tan θ
  • cos θ = 1/sec θ
  • tan θ = 1/cot θ
  • sin θ = 1/cosec θ

Formulas That Involve Periodic Identities (in Radians)

Trigonometry formulas involving periodic identities are used to change angles using p/2, 2p, p, etc. Each trigonometric identity is intrinsically cyclic, which means they repeat themselves after some time. 

This time frame differs for various trigonometry equations on periodic identities. For instance, tan 30deg equals tan 200%, but this isn’t the case for cos 210deg and 30deg. It is possible to use the trigonometry formulas below to confirm the periodicity of cosine and sine functions.

How can I Remember Trigonometry Formulas?

Numerous formulas within the upper classes could make it difficult for us to recall. Also, not consolidated learning these formulas means directly losing a lot of marks in the exams!

Therefore there are a few steps to follow to remember the following:

1. Learn about mathematical symbols.

2. Then is the structure of the formulas and the way they are calculated.

3. Do the exercises regularly.

4. Make flashcards of the formulas, revise, and then finally test your understanding.


This article discussed trigonometry formulas, such as fundamental formulas, reciprocal identities, trigonometric ratio table periodic identity, cofunction identity, differences and sum identities, half-angle identities, angle identities, and triple-angle, as well as the sum of the product identities. We talked about how to master the trigonometry formulas, followed by an explanation of the Inverse trigonometry equation. Then, we talked about the trigonometry table and our trigonometry formulas lists.

Apart from that, if you are interested to know about Surface Area of the Cube then visit our Education category.

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Abdul Waheed
I am Abdul Waheed. I am an SEO expert and tech-savvy. It is my passion to write blogs on almost every topic. I write creative blogs on different categories like lifestyle, modern technology food, cryptocurrency, gaming, entertainment, and many more. Over the past several years, I have written amazing blogs for my websites. Our website provides you with accurate and up-to-date information about what is happening in the world. I enjoy writing because it reminds me that "Words Matter!"