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Trigonometry Formulas involve trigonometric identities that are used to solve several mathematical equations. Trigonometry in Mathematics deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

Trigonometry formulas can solve problems with trigonometric ratios, namely, sine, cosine, tangent, cotangent, secant, cosecant and Pythagorean identities. Understanding and learning these trigonometry formulas is essential for classes 10, 11, and 12 because these formulas help solve equations quickly. Significantly, you understand these Class 10 trigonometry formulas for conceptual understanding

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## Trigonometry Formulas PDF

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Trigonometry formulas provided below can help students get acquainted with different formulas, which can be helpful in solving questions on trigonometric with ease.

## Trigonometry Formulas for Functions, Ratios and Identities and Complementary Angles

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In Mathematics, trigonometry is the most important topic to learn. Trigonometry is basically the study of triangles where ‘Trigon’ means triangle and ‘metry’ means measurement.
Also, trigonometry formulas list is created on the basis of trigonometry ratios such as sine, cosine and tangent. These formulas are used to solve various trigonometry problems. We share all information about Trigonometric Formula PDF, Trigonometry Formula PDF Download.
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Value of Trigonometric Ratios

Taking an example of the right angle triangle, trigonometry formulas list is made. All the trigonometric formulas are based on trigonometric identities and trigonometric ratios. The relationship between angles and length of the sides of the triangle is formulated with the help of trigonometry concepts.

## Trigonometry Formula PDF

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Multiple Trigonometry Formulas Class 10th could be required to solve the problem, so practice to make sure you know when to use each of these formulae.
Trigonometry is a branch of Mathematics that majorly deals with triangles. Trigonometry is also known as the study of relationships between lengths and angles of triangles; sometimes, it also deals with circles. We share Trigonometry Formulas in PDF, Trigonometry Formulas PDF Download.
There is an enormous number of uses of trigonometry and formula of trigonometry. For example, the technique of triangulation is used in geography to measure the distance between landmarks; in astronomy, to measure the distance to nearby stars and also in satellite navigation systems.

### Important Trigonometry Formula

No.-1. Maths Formulas – Trigonometric Ratios and identities are very useful and learning the below formulae help in solving the problems better.
No.-2. Trigonometry is the study of relationships that deal with angles, lengths and heights of triangles and relations between different parts of circles and other geometrical figures.
No.-3. Applications of trigonometry are also found in engineering, astronomy, Physics and architectural design.
No.-4. Trigonometric identities are very useful and learning the below formulae help in solving the problems better.
No.-5. There is an enormous number of fields where these identities of trigonometry and formula of trigonometry are used.
No.-6. Now to get started let us start with noting the difference between Trigonometric identities and Trigonometric Ratios.
No.-7. Trigonometric Identities are some formulas that involve the trigonometric functions. These trigonometry identities are true for all values of the variables.
No.-8. Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the side of the right triangle.
No.-9. Now let us start with the basic formulas of trigonometry and see the basic relationships on which the whole concept is based on.

### Trigonometry Formula Class 10

Trigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, function, identities, formulas to solve problems based on it, especially for right-angled triangles. We share Trigonometry Formulas for Class 10 PDF Download, 10th Class Trigonometry Formulas for Class 10, Trigonometric Identities Class 10 Formula, How to Learn Trigonometry Formulas Class 10, Trigonometry Formulas for Class 10 SSC, 100 Trigonometry Formulas.
Relationship in Trigonometry formula
No.-1. Sin θ = 1 / cosec θ
No.-2. cosec θ = 1 / Sin θ
No.-3. cos θ = 1 / sec θ
No.-4. sec θ = 1/ cos θ
No.-5. sin θ.cosec θ = 1
No.-6. cos θ.sec θ = 1
No.-7. tan θ.cot θ = 1
No.-8. tan θ = sin θ / cos θ
No.-9. cot θ = cos θ / sin θ
No.-10. tan θ = 1 / cot θ
No.-11. cot θ= 1 / tan θ
पायथागॉरियन सूत्र (Pythagorean Identity Formula )
No.-1. sin2 θ + cos2 θ = 1
No.-2. sec2 θ = tan2 θ + 1
No.-3. cosec2 θ =1 + cot2θ

त्रिकोणमिति के कोण और माप  (Trigonometric Angle and Measurements)
No.-1. sin (90° – θ) = cos θ
No.-2. cos (90° – θ) = sin θ
No.-3. tan (90° – θ) = cot θ
No.-4. cosec (90° – θ) = sec θ
No.-5. sec (90° – θ) = cosec θ
No.-6. cot (90° – θ) = tan θ
No.-7. sin (90° + θ) = cos θ
No.-8. cos (90° + θ) = – sin θ
No.-9. tan (90° + θ) = – cot θ
No.-10. cosec (90° + θ) = sec θ
No.-11. sec (90° + θ) = – cosec θ
No.-12. cot (90° + θ) = – tan θ
No.-13. sin (180° – θ) = sin θ
No.-14. cos (180° – θ) = – cos θ
No.-15. tan (180° – θ) = – tan θ
No.-16. cosec (180° – θ) = cosec θ
No.-17. sec (180° – θ) = – sec θ
No.-18. cot (180° – θ) =  – cot θ
No.-19. sin (180° + θ) = – sin θ
No.-20. cos (180° + θ) = – cos θ
No.-21. tan (180° + θ) = tan θ
No.-22. cosec (180° + θ) = – cosec θ
No.-23. sec (180° + θ) = – sec θ
No.-24. cot (180° + θ) =  cot θ
No.-25. sin (360° –  θ) = – sin θ
No.-26. cos (360° –  θ) = cos θ
No.-27. tan (360° –  θ= – tan θ
No.-28. cosec (360° –  θ) = – cosec θ
No.-29. sec (360° –  θ) = sec θ
No.-30. cot (360° –  θ= – cot θ
No.-31. sin (360° +  θ) = sin θ
No.-32. cos (360° +  θ) = cos θ
No.-33. tan (360° +  θ= tan θ
No.-34. cosec (360° +  θ) = cosec θ
No.-35. sec (360° +  θ) = sec θ
No.-36. cot (360° +  θ= cot θ

### Trigonometry Formula List PDF

Relation Between Trigonometric Identities

 S.no Identity Relation 1 tanA sinA/cosA 2 cotA cosA/sinA 3 cosecA 1/sinA 4 secA 1/cosA

The Trigonometric properties are given below

 S.no Property Mathematical value 1 sinA P/H 2 cosA B/H 3 tanA P/B 4 cotA B/P 5 cosecA H/P 6 secA H/B

Trigonometric Identities

sin2A+cos2A=1

tan2A+ 1 =sec2A

cot2A+ 1 = cosec2A

### Trigonometry Formulas for SSC CGL Exam PDF

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### Formulas of Trigonometry

Formulas of Trigonometry:- The word trigonometry is the combination of two Greek words Trigon meaning triangle and metron meaning measure. The term Formulas on Trigonometry means measuring the sides of a triangle. Trigonometry was developed to solve geometric problems involving triangles. Formulas in Trigonometry was studied by sea captains for navigation and surveyors to study the lands. Trigonometry has its applications in various fields like electronics, oceanography, analyzing musical tone, astronomy, and many other areas. In Trigonometry, different types of problems can be solved using Formulas of Trigonometry.
Trigonometric Identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
Trigonometric Ratio relationship between the measurement of the angles and the length of the side of the right triangle. These formulas relate lengths and areas of particular circles or triangles. On the next page you’ll find identities. The identities don’t refer to particular geometric figures but hold for all angles.
The Difference Between Trigonometric Identities And Trigonometric Ratios
Trigonometric Identities: Formula of trigonometry class 12 involves trigonometric functions and trigonometric identities. These identities of trigonometry are accurate for all variable’s values.
Trigonometric Ratio: The relationship of the angle measurement and the right-angle triangle side length is known for its trigonometric ratio.

### Formulas on Trigonometry

Trigonometric Ratios Of Complementary Angles
No.-1. sin(π/2−$$\theta$$) = $$\cos \theta$$
No.-2. cos(π/2−$$\theta$$) = $$\sin \theta$$
No.-3. tan(π/2−$$\theta$$) = $$\cot \theta$$
No.-4. cot(π/2−$$\theta$$) = $$\tan \theta$$
No.-5. sec(π/2−$$\theta$$) = cosec$$\theta$$
No.-6. cosec(π/2−$$\theta$$) = $$\sec \theta$$
No.-1. sin(π−$$\theta$$) = $$\sin \theta$$
No.-2. cos(π−$$\theta$$) = -$$\cos \theta$$
No.-3. tan(π−$$\theta$$) = -$$\tan \theta$$
No.-4. cot(π−$$\theta$$) = -$$\cot \theta$$
No.-5. sec(π−$$\theta$$) = -sec$$\theta$$
No.-6. cosec(π−$$\theta$$) = cosec$$\theta$$
No.-1. sin(π+$$\theta$$) = -$$\sin \theta$$
No.-2. cos(π+$$\theta$$) = -$$\cos \theta$$
No.-3. tan(π+$$\theta$$) = $$\tan \theta$$
No.-4. cot(π+$$\theta$$) = $$\cot \theta$$
No.-5. sec(π+$$\theta$$) = -sec$$\theta$$
No.-6. cosec(π+$$\theta$$) = -cosec$$\theta$$
No.-1. sin(2π−$$\theta$$) = -$$\sin \theta$$
No.-2. cos(2π−$$\theta$$) = $$\cos \theta$$
No.-3. tan(2π−$$\theta$$) = -$$\tan \theta$$
No.-4. cot(2π−$$\theta$$) = -$$\cot \theta$$
No.-5. sec(2π−$$\theta$$) = sec$$\theta$$
No.-6. cosec(2π−$$\theta$$) = -cosec$$\theta$$

Trigonometry formulas list will be helpful for students to solve trigonometric problems easily. Below is the list of formulas based on the right-angled triangle and unit circle which can be used as a reference to study trigonometry.

#### SSC Trigonometry Formula

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It is strongly recommended that you pay close attention to this topic as it will help you enhance your basic concepts and further understand difficult mathematical equations easily. With this, you can easily score high marks in your class 10th, 11th and 12th examinations. Also, make sure that you first understand the formulas, and only then try to memorise them. So, even if you forget during the examination, you can at least solve the equation because you will be well-versed with the basic concept behind the equation.

#### We define the following six Trigonometric Ratios

Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding. Problems involving angles and distances in one plane are covered in plane trigonometry. Applications to similar problems in more than one plane of three-dimensional space are considered in spherical trigonometry.

No.-1. sin⁡θ=Perpendicular/Hypotenuse=y/r
No.-2. cos⁡θ=Base/Hypotenuse=x/r
No.-3. tan⁡θ=Perpendicular/Base=y/x
No.-4. cosec⁡θ=Hypotenuse/Perpendicular=r/y
No.-5. sec⁡θ=Hypotenuse/Base=r/x
No.-6. cot⁡θ=Base/Perpendicular=x/y

#### Important Trigonometry Formulas PDF for Competitive Exams

No.-1. sin^2⁡θ+cos^2⁡θ=1
No.-2. cosec^2⁡θ-cot^2⁡θ=1
No.-3. sec^2⁡θ=tan^2⁡θ=1
No.-4. sin⁡(90°-θ)=cos⁡θ
No.-5. cos⁡(90°-θ)=sin⁡θ
No.-6. tan⁡(90°-θ)=cot⁡θ⇒ cot⁡〖(90°-θ)=tan⁡θ 〗
No.-7. cosec⁡(90°-θ)=sec⁡θ
No.-8. sec⁡(90°-θ)=cosec⁡θ
Here are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, co-secant, tangent and co-tangent.
No.-1. sin θ = Opposite Side/Hypotenuse
No.-2. cos θ = Adjacent Side/Hypotenuse
No.-3. tan θ = Opposite Side/Adjacent Side
No.-4. sec θ = Hypotenuse/Adjacent Side
No.-5. cosec θ = Hypotenuse/Opposite Side
No.-6. cot θ = Adjacent Side/Opposite Side

#### Trigonometric Formulas PDF

These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called co-function identities.
No.-1. sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
No.-2. sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
No.-3. sin (3π/2 – A)  = – cos A & cos (3π/2 – A)  = – sin A
No.-4. sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A
No.-5. sin (π – A) = sin A &  cos (π – A) = – cos A
No.-6. sin (π + A) = – sin A & cos (π + A) = – cos A
No.-7. sin (2π – A) = – sin A & cos (2π – A) = cos A
No.-8. sin (2π + A) = sin A & cos (2π + A) = cos A
Co-function Identities (in Degrees)
The co-function or periodic identities can also be represented in degrees as:
No.-1. sin(90°−x) = cos x
No.-2. cos(90°−x) = sin x
No.-3. tan(90°−x) = cot x
No.-4. cot(90°−x) = tan x
No.-5. sec(90°−x) = csc x
No.-6. csc(90°−x) = sec x
Sum & Difference Identities
No.-1. sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
No.-2. cos(x+y) = cos(x)cos(y)–sin(x)sin(y)
No.-3. tan(x+y) = (tan x + tan y)/ (1−tan x •tan y)
No.-4. sin(x–y) = sin(x)cos(y)–cos(x)sin(y)
No.-5. cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
No.-6. tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)

#### SSC Mathematics Handwritten Notes PDF

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#### Trigonometry Formulas: Important FAQs

Q1: What trigonometry formulas should I study for the SSC CHSL?
Ans: For SSC CHSL, you should study trigonometry formulas either from your Class 10 textbook or from this article.
Q2: What are all the formulas of trigonometry?
Ans: You can learn all the trigonometry formulas from this article. You will get to know about:
– Reciprocal Relationship Between Trigonometric Functions
– Trigonometric Ratios Of Complementary Angles
– Periodicity Identities
– Trigonometric Identities
– Signs Of Trigonometric Functions
– Trigonometric Functions Of Sum And Difference Of Two Angles
– Trigonometry Formulas Involving Product Identities
Q3: How do I memorize maths trigonometry formulas?
Ans: Our academic experts advise you not to memorize these trigonometry formulas. The more you try to learn consciously, the more is the chance that you are going to forget it. The best way to learn these formulas is to write them on a piece of paper and refer to them while you solve the questions. This way you will be able to easily learn the Trigonometry formulas.
Q4: Can I get a trigonometry formulas list?
Ans: Yes, with the help of this article, you can get all the important trigonometry formulas in one place.
Q.-5. What are the basic trigonometric ratios?
Ans. There are six trigonometric ratios. Those are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant.
Q.-6. What are the three main functions in trigonometry?
Ans. Three main functions in trigonometry are Sin, Cos, and Tan.
Q.-7. What are the fundamental trigonometry identities?
Ans. Fundamental trigonometry identities are
No.-1. sin2 A + cos2 A = 1
No.-2. 1+tan2 A = sec2 A
No.-3. 1+cot2 A = csc2 A

##### Details of Trigonometry Notes PDF
1. Subject – Mathematics Notes
2. Topic – Trigonometry
3. Format – PDF
4. Type –Typewritten

Trigonometry Formulas PDF Part 1.

Trigonometry Formulas PDF Part 2