Trigonometry Formulas and Identities, Check Concepts, Tips, and Practice Questions

Safalta expert Published by: Saksham Chauhan Updated Thu, 25 Aug 2022 02:04 AM IST

Highlights

See the article below for the trigonometry formulae and trigonometry formula tricks. Candidates should review this information for tips on using trigonometric formulas.

One area of mathematics that involves a lot of formulae is trigonometry, and you can only solve questions on this subject if you are well-versed in the formulas and identities. There are various trigonometric ratios, formulas, and identities, including half-angle, double-angle, product, sum, and difference identities. It is crucial to comprehend and memorise these identities if you wish to learn trigonometry.Here we have provided the list of all important trigonometric formulas, identities, and more. If you are preparing for competitive exams and are looking for expert guidance, you can check out our monthly FREE Current Affairs E-book- Download Now. Also,  download our app- 'Exam Taiyari App' and boost your preparation. FREE GK EBook- Download Now.

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Table of content 

  1. Trigonometry Formulas 2022
  2. Important Identities of Trigonometric Ratios
  3. Ratios in Trigonometry
  4. Trigonometric ratio relationships
  5. Trigonometric ratio values for each quadrant
  6. Different Trigonometric Ratio Specific Angle Values
  7. Relationship between the squares of several types of trigonometric ratios in trigonometry
  8. Important Idea to Address a Particular Type of Question
  9. Tangent Trigonometry Formulas
  10. Maximum & Minimum Value in Trigonometry 
    Highest & Lowest Value

Trigonometry Formulas 2022

There are six trigonometric operations: Sin, Cos, Tan, Sec, Cosec, and Cot. Trigonometric ratios can be used to derive the current length and angle. All trigonometry formulae, formula tricks, and questions are built upon these six functions. Aspirants have access to information about trigonometry, including formulas, tips for using trigonometry formulas, and questions. There are questions about trigonometry in several competitive exams, including the SSC, Railway, and others.

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This website has notes on formula trigonometry that are useful for exams. You can use it to help you master the basic trigonometric formulas. Below is a complete collection of all the trigonometric formulas for classes 10 and 11, as well as for classes 12 and 13.

Important Identities of Trigonometric Ratios

To learn the basics of trigonometry, you must be aware of all significant trigonometric ratios and their identities.

Ratios in Trigonometry

We will make advantage of a right-angled triangle to learn several trigonometric ratio functions. Assume that the angle A of the right-angled triangle ABC is 90 degrees.


Trigonometric ratio relationships

 

Trigonometry Formulas 2022, List of Tricks And Identities_50.1 

 

 

Trigonometry Formulas 2022, List of Tricks And Identities_60.1

Trigonometric ratio values for each quadrant

Trigonometry Formulas 2022, List of Tricks And Identities_70.1

Different Trigonometric Ratio Specific Angle Values

To answer the question based on the trigonometric ratio of the angles 0°, 30°, 45°, and 60°, you must become familiar with the following table.

Trigonometry Formulas 2022, List of Tricks And Identities_80.1

Relationship between the squares of several types of trigonometric ratios in trigonometry

Trigonometry Formulas 2022, List of Tricks And Identities_90.1

Important Idea to Address a Particular Type of Question

If A + B = 90°

Results that are true always :

(i)  sin A.

sec B = 1 or  sin A = cos B

(ii) cos A. cosec B = 1 or  sec A = cosec B

(iii) tan A. tan B = 1  or tan A = cot B

(iv) cot A. cot B = 1

(v)  sin²A + sin² B = 1

(vi) cos² A + cos² B = 1

Formula for the Sum and Difference of Two Angles in Trigonometry, an Important Formula

(1) sin (A+B) =sinA. cosB + cosA sinB

(2) sin(A – B) =sinA. cosB – cosA sinB

(3) cos(A+B) =cosA. cosB – sinA sinB

(4) cos(A-B) = cosA. cosB+sinA sinB

(5) 2 sinA.cosB = sin(A+B)+sin (A-B)

(6) 2 cosA. sinB = sin(A+B)-sin (A-B)

(7) 2 sinA. sinB = cos(A-B)-cos(A+B)

(8) 2 cosA.cosB = cos(A+B)+cos(A-B)

(9) sin²A-sin²B = sin(A+B). sin(A-B)

(10) cos²A-cos²B = cos(A+B).cos (A-B)

Tangent Trigonometry Formulas
Trigonometry Formulas 2022, List of Tricks And Identities_100.1
List of trigonometric formulas 

If A + B + C equals 180 degrees, then A + B + C equals A. B. C. 

If A + B + C = 90°, then A + B + C must also equal A cot B cot C. 

If sin(a) + cosec(a) = 2,

Then, Trigonometry Formulas 2022, List of Tricks And Identities_110.1

Trigonometry Formulas 2022, List of Tricks And Identities_120.1

Trigonometry Formulas 2022, List of Tricks And Identities_130.1

Maximum & Minimum Value in Trigonometry 
Highest & Lowest Value

The two extremes are Minimum and Maximum 

                                                     Minimum                           Maximum

  • sin θ, cos θ [odd power]             –1                                         +1
  • sin θ, cos θ [even power]             0                                         +1
  • tan θ, cot θ [odd power]             –∞                                       +∞
  • tan θ, cot θ [even power]             0                                        +∞
  • sec θ, cosec θ [odd power]         –∞                                       +∞
  • sec θ, cosec θ [even power]        +1                                        +∞

Trigonometry Formulas 2022, List of Tricks And Identities_140.1 Trigonometry Formulas 2022, List of Tricks And Identities_150.1 Trigonometry Formulas 2022, List of Tricks And Identities_160.1 Trigonometry Formulas 2022, List of Tricks And Identities_170.1 Trigonometry Formulas 2022, List of Tricks And Identities_180.1Trigonometry Formulas 2022, List of Tricks And Identities_190.1 Trigonometry Formulas 2022, List of Tricks And Identities_200.1

Who is the father of trigonometry?

Hipparchus of Nicaea

What are the symbols in trigonometry?

Symbol Name Explanation Example
crd θ Chord function (Length of chord subtended by angle in unit circle) crd θ ≥ sin ⁡
Cosine function ⁡ θ + cos 2 ⁡
tan ⁡ Tangent function ⁡ ⁡ ⁡
Cosecant function ⁡ θ = 1 sin ⁡

Who invented trigonometry in India?

Aryabhata I

What is the Trigonometric ratio values for each quadrant ?

Trigonometry Formulas 2022, List of Tricks And Identities_70.1

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