Trigonometry formulas for class 12

Chapter 2 Inverse Trigonometric Functions Formulas Students might already have some basic idea about Trigonometric from their previous classes. In Class 12, students will learn more advanced concepts of Inverse Trigonometric Functions. Practicing NCERT notes can be a great way to prepare for competitive exams. Students should go through all exercises to score higher marks. Vidyakul provides NCERT notes for Class 12 with over 1500 questions for practice and 9 books for reference. It will play an important role in helping the students prepare for the exams. Read further to know more. MATHEMATICS NOTES CHAPTER-2 Points to Remember Below we have provided some of the important points to remember for this chapter to ace the exams: • Inverse trigonometric functions have a principal value that falls within the range of the principal value branch. • Trigonometric functions cannot be represented with inverse trigonometric functions as reciprocals. • The value that lies in the principal branch range is the principal value of a trigonometric function. • A tangent function can be explained as the inverse of an arctangent function. It is denoted by tan-1x. • The inverse of the tangent function is y = tan-1x (arctangent x). This function is a domain of -∞< x <∞. The range is expressed as -π / 2 < y <π /2. Topics and Sub-topics In this chapter, students will study the restrictions on domains and ranges of trigonometric functions that ensure the existence of their inverses and observe thei...

Trigonometry is a branch of Mathematics that deals mostly with triangles Trigonometry is also known as the study of relationships between the lengths and angles of triangles. Sometimes, it also dealing with circles. There are various uses of trigonometry and the formula of trigonometry. For example, the technique of triangulation is used in Geography to measure the distance between two landmarks. Also, in Astronomy, to measure the distance to nearby stars and many more. In this topic, we will discuss the Trigonometric Functions Formula with some examples. 3 Solved Examples for Trigonometric Functions Formula Concept of Trigonometry Trigonometry is the study of the relationships which involves angles, lengths, and heights of triangles. It also relations the different parts of circles and other geometrical figures. Applications of trigonometry are also found in engineering, astronomy, Physics and many other areas of study. Trigonometric Identities are popular formulas that involve trigonometric functions. These identities are true for all values of the variables. Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the side of the right triangle. There are six functions which are the core of trigonometry. There are three primary ratios given as bellow: • Sine (sin) • Cosine (cos) • Tangent (tan) The other three are not used as often but can be derived from the three primary functions. These derived functions are: • Secant ...

Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important You are here Important Deleted for CBSE Board 2024 Exams Important Deleted for CBSE Board 2024 Exams Important Deleted for CBSE Board 2024 Exams Important Deleted for CBSE Board 2024 Exams Check the formula sheet of integration. Topics include • Basic Integration Formulas • Integral of special functions • Integral by Partial Fractions • Integration by Parts • Other Special Integrals • Area as a sum • Properties of definite integration Integration of Trigonometric Functions, Properties of Definite Integration are all mentioned here. Basic Formula • ∫x n = x n+1 /n+1 + C • ∫cos x = sin x + C • ∫sin x = -cos x + C • ∫sec 2 x = tan x + C • ∫cosec 2 x = -cot x + C • ∫sec x tan x = sec x + C • ∫cosec x cot x = -cosec x + C • ∫dx/√ 1- x 2 = sin -1 x + C • ∫dx/√ 1- x 2 = -cos -1 x + C • ∫dx/√ 1+ x 2 = tan -1 x + C • ∫dx/√ 1+ x 2 = -cot -1 x + C • ∫e x = e x + C • ∫a x = a x / log a + C • ∫dx/x √ x 2 - 1= sec -1 x + C • ∫dx/x √ x 2 - 1= cosec -1 x + C • ∫1/x = log |x| + c • ∫tan x = log |sec x| + c • ∫cot x = log |sin x| + c • ∫sec x = log |sec x + tan x| + c • ∫cosec x = log |cosec x - cot x| + c Practice Integrals of some special function s • ∫dx/(x 2 - a 2 ) = 1/2a log⁡ |(x - a) / (x + a)| + c • ∫dx/(a 2 - x 2 ) = 1/2a log⁡ |(a + x) / (a - x)| + c • ∫dx / (x 2 + a 2 ) = 1/...

Pythagorean Identities Signs of sin, cos, tan in different quadrants To learn sign of sin, cos, tan in different quadrants, we remember A dd → S ugar → T o → C offee Representing as a table Quadrant I Quadrant II Quadrant III Quadrant IV sin + + – – cos + – – – tan + – + – Radians Radian measure = π/180 × Degree measure Also, 1 Degree = 60 minutes i.e. 1° = 60’ 1 Minute = 60 seconds i.e. 1’ = 60’’ Negative angles (Even-Odd Identities) sin (–x) = – sin x cos (–x) = cos x tan (–x) = – tan x sec (–x) = sec x cosec (–x) = – cosec x cot (–x) = – cot x Value of sin, cos, tan repeats after 2π sin (2π + x) = sin x cos (2π + x) = cos x tan (2π + x) = tan x Shifting angle by π/2, π, 3π/2 (Co-Function Identities or Periodicity Identities) sin (π/2 – x) = cos x cos (π/2 – x) = sin x sin (π/2 + x) = cos x cos (π/2 + x) = – sin x sin (3π/2 – x) = – cos x cos (3π/2 – x) = – sin x sin (3π/2 + x) = – cos x cos (3π/2 + x) = sin x sin (π – x) = sin x cos (π – x) = – cos x sin (π + x) = – sin x cos (π + x) = – cos x sin (2π – x) = – sin x cos (2π – x) = cos x sin (2π + x) = sin x cos (2π + x) = cos x Angle sum and difference identities Double Angle Formulas Triple Angle Formulas Half Angle Identities (Power reducing formulas) Sum Identities (Sum to Product Identities) Product Identities (Product to Sum Identities) Product to sum identities are 2 cos⁡x cos⁡y = cos⁡ (x + y) + cos⁡(x - y) -2 sin⁡x sin⁡y = cos⁡ (x + y) - cos⁡(x - y) 2 sin⁡x cos⁡y = sin⁡ (x + y) + sin⁡(x - y) 2 cos⁡x sin⁡y = sin⁡ ...

Trigonometry is a field of mathematics concerned with the connections between triangle side lengths and angles. The word trigonometry is made by the Greek word trigonon, "triangle," and metron, "measure". Applications of geometry to astronomical research gave rise to the discipline in the Hellenistic culture during the 3rd century BC. The Greeks concentrated on chord calculations, whereas Indian mathematicians developed the first tables of values for trigonometric ratios (also known as trigonometric functions) as a sine. Trigonometry has been used in geodesy, surveying, celestial mechanics, and navigation throughout history. Trigonometry has a lot of different identities. These trigonometric identities are frequently used to rewrite trigonometric formulas to simplify them, discover a more usable form of them, or solve an equation. The six important trigonometric functions are sine, cos, tan, cosec, sec, and cot. This article will cover the trigonometry table formula, trigonometry questions, trigonometry examples, and the real-life applications of trigonometry. What is trigonometry Trigonometry is considered to be one of the most important branches in mathematics. By combining the words 'Trigonon' and 'Metron' we are introduced to the word trigonometry. Trigonometry is the study of the relationship between the sides and angles of a right triangle. Trigonometry also helps in finding and measuring the unknown dimensions of a right-angled triangle by using formulas and identit...

Chapter 2 Inverse Trigonometric Functions Formulas Students might already have some basic idea about Trigonometric from their previous classes. In Class 12, students will learn more advanced concepts of Inverse Trigonometric Functions. Practicing NCERT notes can be a great way to prepare for competitive exams. Students should go through all exercises to score higher marks. Vidyakul provides NCERT notes for Class 12 with over 1500 questions for practice and 9 books for reference. It will play an important role in helping the students prepare for the exams. Read further to know more. MATHEMATICS NOTES CHAPTER-2 Points to Remember Below we have provided some of the important points to remember for this chapter to ace the exams: • Inverse trigonometric functions have a principal value that falls within the range of the principal value branch. • Trigonometric functions cannot be represented with inverse trigonometric functions as reciprocals. • The value that lies in the principal branch range is the principal value of a trigonometric function. • A tangent function can be explained as the inverse of an arctangent function. It is denoted by tan-1x. • The inverse of the tangent function is y = tan-1x (arctangent x). This function is a domain of -∞< x <∞. The range is expressed as -π / 2 < y <π /2. Topics and Sub-topics In this chapter, students will study the restrictions on domains and ranges of trigonometric functions that ensure the existence of their inverses and observe thei...

Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important Important You are here Important Deleted for CBSE Board 2024 Exams Important Deleted for CBSE Board 2024 Exams Important Deleted for CBSE Board 2024 Exams Important Deleted for CBSE Board 2024 Exams Check the formula sheet of integration. Topics include • Basic Integration Formulas • Integral of special functions • Integral by Partial Fractions • Integration by Parts • Other Special Integrals • Area as a sum • Properties of definite integration Integration of Trigonometric Functions, Properties of Definite Integration are all mentioned here. Basic Formula • ∫x n = x n+1 /n+1 + C • ∫cos x = sin x + C • ∫sin x = -cos x + C • ∫sec 2 x = tan x + C • ∫cosec 2 x = -cot x + C • ∫sec x tan x = sec x + C • ∫cosec x cot x = -cosec x + C • ∫dx/√ 1- x 2 = sin -1 x + C • ∫dx/√ 1- x 2 = -cos -1 x + C • ∫dx/√ 1+ x 2 = tan -1 x + C • ∫dx/√ 1+ x 2 = -cot -1 x + C • ∫e x = e x + C • ∫a x = a x / log a + C • ∫dx/x √ x 2 - 1= sec -1 x + C • ∫dx/x √ x 2 - 1= cosec -1 x + C • ∫1/x = log |x| + c • ∫tan x = log |sec x| + c • ∫cot x = log |sin x| + c • ∫sec x = log |sec x + tan x| + c • ∫cosec x = log |cosec x - cot x| + c Practice Integrals of some special function s • ∫dx/(x 2 - a 2 ) = 1/2a log⁡ |(x - a) / (x + a)| + c • ∫dx/(a 2 - x 2 ) = 1/2a log⁡ |(a + x) / (a - x)| + c • ∫dx / (x 2 + a 2 ) = 1/...

Pythagorean Identities Signs of sin, cos, tan in different quadrants To learn sign of sin, cos, tan in different quadrants, we remember A dd → S ugar → T o → C offee Representing as a table Quadrant I Quadrant II Quadrant III Quadrant IV sin + + – – cos + – – – tan + – + – Radians Radian measure = π/180 × Degree measure Also, 1 Degree = 60 minutes i.e. 1° = 60’ 1 Minute = 60 seconds i.e. 1’ = 60’’ Negative angles (Even-Odd Identities) sin (–x) = – sin x cos (–x) = cos x tan (–x) = – tan x sec (–x) = sec x cosec (–x) = – cosec x cot (–x) = – cot x Value of sin, cos, tan repeats after 2π sin (2π + x) = sin x cos (2π + x) = cos x tan (2π + x) = tan x Shifting angle by π/2, π, 3π/2 (Co-Function Identities or Periodicity Identities) sin (π/2 – x) = cos x cos (π/2 – x) = sin x sin (π/2 + x) = cos x cos (π/2 + x) = – sin x sin (3π/2 – x) = – cos x cos (3π/2 – x) = – sin x sin (3π/2 + x) = – cos x cos (3π/2 + x) = sin x sin (π – x) = sin x cos (π – x) = – cos x sin (π + x) = – sin x cos (π + x) = – cos x sin (2π – x) = – sin x cos (2π – x) = cos x sin (2π + x) = sin x cos (2π + x) = cos x Angle sum and difference identities Double Angle Formulas Triple Angle Formulas Half Angle Identities (Power reducing formulas) Sum Identities (Sum to Product Identities) Product Identities (Product to Sum Identities) Product to sum identities are 2 cos⁡x cos⁡y = cos⁡ (x + y) + cos⁡(x - y) -2 sin⁡x sin⁡y = cos⁡ (x + y) - cos⁡(x - y) 2 sin⁡x cos⁡y = sin⁡ (x + y) + sin⁡(x - y) 2 cos⁡x sin⁡y = sin⁡ ...

Trigonometry is a branch of Mathematics that deals mostly with triangles Trigonometry is also known as the study of relationships between the lengths and angles of triangles. Sometimes, it also dealing with circles. There are various uses of trigonometry and the formula of trigonometry. For example, the technique of triangulation is used in Geography to measure the distance between two landmarks. Also, in Astronomy, to measure the distance to nearby stars and many more. In this topic, we will discuss the Trigonometric Functions Formula with some examples. 3 Solved Examples for Trigonometric Functions Formula Concept of Trigonometry Trigonometry is the study of the relationships which involves angles, lengths, and heights of triangles. It also relations the different parts of circles and other geometrical figures. Applications of trigonometry are also found in engineering, astronomy, Physics and many other areas of study. Trigonometric Identities are popular formulas that involve trigonometric functions. These identities are true for all values of the variables. Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the side of the right triangle. There are six functions which are the core of trigonometry. There are three primary ratios given as bellow: • Sine (sin) • Cosine (cos) • Tangent (tan) The other three are not used as often but can be derived from the three primary functions. These derived functions are: • Secant ...

In this unit, you'll explore the power and beauty of trigonometric equations and identities, which allow you to express and relate different aspects of triangles, circles, and waves. You'll learn how to use trigonometric functions, their inverses, and various identities to solve and check equations and inequalities, and to model and analyze problems involving periodic motion, sound, light, and more.