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.
Also check ,
Percentage Formula , Steps to calculate percentage
Geometry Definition, Formulas, and Shapes: What Is It?
Also check ,
Percentage Formula , Steps to calculate percentage
Geometry Definition, Formulas, and Shapes: What Is It?
Table of content
- Trigonometry Formulas 2022
- Important Identities of Trigonometric Ratios
- Ratios in Trigonometry
- Trigonometric ratio relationships
- Trigonometric ratio values for each quadrant
- Different Trigonometric Ratio Specific Angle Values
- Relationship between the squares of several types of trigonometric ratios in trigonometry
- Important Idea to Address a Particular Type of Question
- Tangent Trigonometry Formulas
- 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. 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
Trigonometric ratio values for each quadrant
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.
Relationship between the squares of several types of trigonometric ratios in trigonometry
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
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,
If A + B + C = 90°, then A + B + C must also equal A cot B cot C.
If sin(a) + cosec(a) = 2,
Then,
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 +∞
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 ?
Quadrant I Quadrant II Quadrant III Quadrant IV
sin θ +ve +ve -ve -ve
cos θ +ve -ve -ve +ve
tan θ +ve -ve +ve -ve
cosec θ +ve +ve -ve -ve
sec θ +ve -ve -ve +ve
cot θ +ve -ve +ve -ve
sin θ +ve +ve -ve -ve
cos θ +ve -ve -ve +ve
tan θ +ve -ve +ve -ve
cosec θ +ve +ve -ve -ve
sec θ +ve -ve -ve +ve
cot θ +ve -ve +ve -ve