Trigonometric Functions

Edited By Team Careers360 | Updated on Aug 14, 2023 04:44 PM IST

Introduction:
One of the most important concepts in mathematics is trigonometry. The measuring of angles and sides of a triangle is the subject of trigonometry. Normally, trigonometry is used to solve problems with right-angled triangles. Its functions are also used to calculate the length of a circle's arc, which is a portion of a circle with a radius and a centre point.

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When we break down the word trigonometry, we find that 'Tri' is a Greek word that means three,' 'Gon' means length,' and metry' means trigonometric formulas measurement.' Trigonometry, in its simplest form, is the study of triangles with angles and lengths on their sides. The sin 0, sin 30, sin 45 , sin 60, sin 90, sin 180 and cosine formula such as cosine of 0, cosine of 30, cosine of 45, cosine of 60, cosine of 90, cosine of 180 tangent and trigonometric formulas class 10 are the foundations of trigonometry.

Trigonometry for class 10 and trigonometric formulas class 11 consists of trigonometric functions trigonometric identities class 10 that can be used to simplify the solution of complicated problems.

List of topics according to NCERT and JEE Main/NEET syllabus:

Angle.
Positive and Negative Angles
Measurement of Angles
1. Sexagesimal System/Degree Measure (English System)
2. Centesimal System (French System)
3. Circular System (Radian System)
Relationship.
Trigonometric Ratios.
Trigonometric (or Circular) Functions.
Domain and Range
Range of Modulus Functions
Trigonometric Identities
Sign of Trigonometric Ratios
1. Trigonometric Ratios of Some Standard Angles
2. Trigonometric Ratios of Some Special Angles
3. Trigonometric Ratios of Allied Angles
Trigonometric Periodic Functions.
Maximum and Minimum Values of Trigonometric Expressions
Trigonometric Ratios of Compound Angles
Transformation Formulae
1. Trigonometric Ratios of Multiple Angles
2. Trigonometric Ratios of Some Useful Angles
Hyperbolic Functions
1. Domain and Range of Hyperbolic Function
Formulae for the Sum and Difference
Formulae to Transform the Product into Sum or Difference
Formulae for Multiples of x

Important concepts and Laws:

The Trigonometry Formula List
Basic Trigonometric Formulas
identities of trigonometry
Reciprocal Identities
Pythagorean Identities
Trigonometric Ratios Table
Periodic Identities
Cofunction Identities (in Degrees)
all formulas of trigonometry
Trigonometry Formulas of Sum and Difference of Identities.
Half Angle Identities
Double Angle Identities
Triple Angle Identities
Product Identities
Sum of Product Identities
inverse trigonometric functions
Inverse Trigonometry Formula
inverse sine and inverse Cosine Laws

NCERT Notes Subject Wise Link:

Importance of trigonometric Functions class 11:

Maths 11 th grade Trigonometry is more than just a subject; it has several applications. In the exam, there will be a pure trigonometric question. Many physics courses need trigonometry, and it can make solving problems much easier and simpler. There will be some questions in math that need mastery of two or three courses. Most of the time, trigonometric equations were employed to confound you in such problems. In a nutshell, to succeed in tests, be thorough with trigonometry. For jee advanced, one should never rely on weightage.

Direct trigonometry queries, on the other hand, are less likely. It will be widely used in physics to create equations, solve problems, and even derive numerous formulae (for example, it will be widely utilised in simple harmonic motion, waves, sound waves, Newton's law, motion in two dimensions, and so on).... As a result, each and every formula, as well as their applications based on trigonometric values, such as where and how they should be applied to solve problems, should be thoroughly memorised.

For jee, trigonometry is a crucial subject.

Although, in the JEE exam, there are just two to three straight questions from trigonometry.

However, it is still very important.

If you are accepted into a good institute, they will begin with log and trigonometry.

The importance of trigonometry is demonstrated in the following subjects. Furthermore, you will see that trigonometry is employed in nearly every subject, including algebra, calculus, triangle properties, geometry, and so on. As a result, a solid understanding of trigonometry is required for JEE preparation. You can gain experience by solving books like SL Loney, which have introductory trigonometry questions. All trigonometric formulas must be memorised.

NCERT Solutions Subject wise link:

NCERT Exemplar Solutions Subject wise link:

Frequently Asked Question (FAQs)

1. What are some tricks for remembering trigonometric formulas in class 11?

In upper levels, we have a lot of formulas that are tough to remember, thus here are a few ways to remember them:

1. Learn how to read mathematical symbols.

2. The structure of the formulas and how they are generated follows.

3. Rehearse the formulas on a regular basis.

4. Review the formulas with flashcards, then revise and test yourself.

2. What is the trigonometry basic formula?

In trigonometry, there are six fundamental trigonometric ratios. Trigonometric functions are another name for these ratios. Sine, cosine, secant, cosecant, tangent, and cotangent are the six essential trigonometric functions. The right-angled triangle is used to generate trigonometric functions and identities. We may use trigonometric formulas to get the sine, cosine, tangent, secant, cosecant, and cotangent values when we know the height and base side of the right triangle.

1. sinθ=OppositeSide/Hypotenuse

2. cosθ=AdjacentSide/Hypotenuse

3. tanθ=OppositeSide/AdjacentSide

4. secθ=Hypotenuse/AdjacentSide

5. cosec θ=Hypotenuse/OppositeSide

6. cotθ=AdjacentSide/OppositeSide

3. What are the eleven trigonometric identities?

The following are the eleven trigonometric identities in trigonometry:

1. Fundamental formulas

2. Identity Reciprocity

3. Ratio trigonometric Table

4. Recurring Identities

5. Identities of Co-functions

6. Identities of Sum and Difference

7. Identities with a Half-Angle

8. Identities with Two Angles

9. Identities with Triple Angles

10 Identities of Products

11. Product Identities as a Whole

4. What is the integral of cosine x?

The integral of cos x is sin x + C. i.e., ∫ cos x dx = sin x + C. Here, C is the integration constant.