Trigonometry Formula

Trigonometry all Formulas List

Trigonometry is the branch of mathematics which deals in measuring the angles, lengths, and heights of the triangle and other geometrical figures. The trigonometry formula can be used to solve the problems in a much better way. They are essential in solving questions related to Trigonometry ratios and Identities.

Trigonometry ratio is defined as the relationship between the measurement of lengths and angles of the right triangle and also be used in the particular areas of the circle. Trigonometry functions can be used to describe the applicability and the relationship of physical phenomena like astronomy, waves, etc.

Vedantu offers a comprehensive trigonometry formulas list to help the students in learning the basic and advanced concepts of trigonometry with ease.

Basics of Trigonometry

In the right-angled triangle, the 3 sides are known as Hypotenuse, Perpendicular (Opposite side) and Base (Adjacent side). The hypotenuse is the longest side of the triangle and is opposite to the right angle.

The list of basic trigonometry formulas
1. $\sin \theta = \frac{{{\text{Perpendicular}}}}{{{\text{hypotenuse}}}}$
2. $\cos \theta = \frac{{{\text{base}}}}{{{\text{hypotenuse}}}}$
3. $\tan \theta = \frac{{{\text{Perpendicular}}}}{{{\text{base}}}}$
4. $\cot \theta = \frac{{{\text{base}}}}{{{\text{Perpendicular}}}}$
5. $\sec \theta = \frac{{{\text{hypotenuse}}}}{{{\text{base}}}}$
6. ${\text{cosec}}\theta = \frac{{{\text{hypotenuse}}}}{{{\text{Perpendicular}}}}$

Reciprocal relation are given as:
${\text{cosec}}\theta = \frac{1}{{\sin \theta }}$
${\text{sec}}\theta = \frac{1}{{\cos \theta }}$
${\text{cot}}\theta = \frac{1}{{\tan \theta }}$
${\text{sin}}\theta = \frac{1}{{{\text{cosec}}\theta }}$
${\text{cos}}\theta = \frac{1}{{\sec \theta }}$
${\text{tan}}\theta = \frac{1}{{\cot \theta }}$

Trigonometric identities
1. ${\sin ^2}\theta + {\cos ^2}\theta = 1$
2. $1 + {\tan ^2}\theta = {\sec ^2}\theta $
3. $1 + {\cot ^2}\theta = {\text{cose}}{{\text{c}}^2}\theta $

Trigonometric ratios of complimentary angles
1. $\sin \left( {90 - \theta } \right) = \cos \theta $
2. $\cos \left( {90 - \theta } \right) = \sin \theta $
3. $\tan \left( {90 - \theta } \right) = \cot \theta $
4. $\cot \left( {90 - \theta } \right) = \tan \theta $
5. $\sec \left( {90 - \theta } \right) = \cos {\text{ec}}\theta $
6. ${\text{cosec}}\left( {90 - \theta } \right) = \sec \theta $

All the maths trigonometry formulas are taken from right-angled triangle where if the lengths of a triangle are given then the student can easily find the sine, cosine, tangent, cosecant, secant and cotangent values.

Once the student learns the basics of trigonometry then learning the advanced level can gradually become easier.

Solved Example for Better Understanding

Example: For a right-angle triangle ABC, the measurement of Angle C is 90 for which angle BAC = θ and sinθ = 4/5. Find the value of cosθ.

Solution: Using the identity, sin2θ + cos2θ = 1
Putting the value of sin in the identity,
(4/5)^2 + cos2θ  =1
cosθ =√1-(4/5)^2 = 3/5

Real Life Applications of Trigonometry
In real life, the trigonometry has been used in applications of various fields such as architects, surveyors, astronauts, physicists, engineers, and even crime scene investigators.

  • • It is used in aviation industries.

  • • It is used in cartography for creating maps

  • • Also, trigonometry can also be used in the applications of satellite systems.

  • Above all, teachers and toppers also recommend studying the trigonometry formulae from Vedantu PDF list as it can save a lot of time in preparing for the exam.

    What to expect from Vedantu?

    Whether you are in Class 6 or Class 12, Vedantu has a list of trigonometry all formulas essential in every syllabus. 

  • • The free of cost formulas can be accessed by the students at any time.

  • • A unique way has been adopted by Vedantu for solving various mathematical problems and equations. It is very helpful for the student to understand the basic use of it rather than just memorizing it.

  • • Students can access important revision notes and questions to practice and learn.

  • • Students of CBSE Board from Class 6 to Class 12 can also download chapter-wise math formulae in PDF format.

  • Students can also download the important study materials from Vedantu like RS Aggarwal Solutions, RD Sharma solutions, NCERT solutions, etc. These can further enhance the concepts of algebra and the application of every formula.