Topics
Relations and Functions
Mathematics
Numbers, Quantification and Numerical Applications
- Modulo Arithmetic
- Apply Arithmetic Operations Using Modular Arithmetic Rules
- Congruence Modulo
- Apply the Definition of Congruence Modulo in Various Problems
- Allegation and Mixture
- Rule of Allegation to Produce a Mixture at a Given Price
- Determine the Mean Price of Amixture
- Apply Rule of Allegation
- Solve Real Life Problems Mathematically
- Boats and Streams
- Express the Boats and Streams Problem in the Form of an Equation
- Pipes and Cisterns
- Races and Games
- Concept of Partnership
- Differentiate Between Active Partner and Sleeping Partner
- Determination of Partner's Ratio
- Volume and Surface Area of Combined Solids
- Numerical Inequalities
Applied Mathematics
Algebra
Inverse Trigonometric Functions
Calculus
Matrices
- Introduction of Matrices
- Matrices
- Matrices Notation
- Order of a Matrix
- Types of Matrices
- Equality of Matrices
- Operations on Matrices
- Addition of Matrices
- Properties of Matrix Addition
- Multiplication of a Matrix by a Scalar
- Properties of Scalar Multiplication of a Matrix
- Multiplication of Matrices
- Properties of Multiplication of Matrices
- Negative of Matrix
- Subtraction of Matrices
- Transpose of a Matrix
- Properties of Transpose of the Matrices
- Symmetric and Skew Symmetric Matrices
- Elementary Transformations of a Matrix
- Invertible Matrices
- Inverse of Matrix
- Inverse of a Matrix by Elementary Transformation
Probability Distributions
Determinants
Continuity and Differentiability
- Introduction of Continuity and Differentiability
- Concept of Continuity
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Implicit Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Mean Value Theorem
Index Numbers and Time Based Data
- Meaning of Index Numbers
- Construction of Index Numbers
- Test of Adequacy of Index Numbers
- Population and Sample
- Differentiate Between Population and Sample
- Representative Sample from a Population
- Parameter
- Statistics
- Relation Between Parameter and Statistic
- Limitations of Statistics to Generalize the Estimation for Population
- Statistical Significance and Statistical Inferences
- Central Limit Theorem
- Relation Between Population, Sampling Distribution, and Sample
- Time Series Analysis
- Components of a Time Series
- Time Series Analysis for Uni-variate Data
Financial Mathematics
- Perpetuity Fund
- Sinking Fund
- Calculate Perpetuity
- Differentiate Between Sinking Fund and Saving Account
- Valuation of Bond
- Calculate Value of Bond Using present Value Approach
- Concept of EMI
- Calculation of EMI
- Linear Method of Depreciation
- Interpretation Cost, Residual Value and Useful Life of an Asset
- Methods of Calculating Depreciation Amount
Applications of Derivatives
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
- Increasing and Decreasing Functions
- Tangents and Normals
- Approximations
- Maxima and Minima
- Maximum and Minimum Values of a Function in a Closed Interval
- Graph of Maxima and Minima
- Simple Problems on Applications of Derivatives
Linear Programming
Integrals
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
- Geometrical Interpretation of Indefinite Integrals
- Some Properties of Indefinite Integral
- Comparison Between Differentiation and Integration
- Methods of Integration: Integration by Substitution
- Methods of Integration: Integration Using Partial Fractions
- Integrals of Some Particular Functions
- Methods of Integration: Integration by Parts
- Integration Using Trigonometric Identities
- Definite Integrals
- Definite Integral as the Limit of a Sum
- Fundamental Theorem of Calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
Applications of the Integrals
Differential Equations
- Introduction of Differential Equations
- Basic Concepts of Differential Equation
- Order and Degree of a Differential Equation
- General and Particular Solutions of a Differential Equation
- Formation of a Differential Equation Whose General Solution is Given
- Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
- Methods of Solving First Order, First Degree Differential Equations
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Solutions of Linear Differential Equation
Vectors
- Introduction of Vector
- Basic Concepts of Vector Algebra
- Vectors and Their Types
- Addition of Vectors
- Properties of Vector Addition
- Multiplication of a Vector by a Scalar
- Components of a Vector
- Vector Joining Two Points
- Section Formula
- Product of Two Vectors
- Scalar (Or Dot) Product of Two Vectors
- Projection of a Vector on a Line
- Vector (Or Cross) Product of Two Vectors
- Magnitude and Direction of a Vector
- Position Vector of a Point Dividing a Line Segment in a Given Ratio
- Scalar Triple Product of Vectors
Three-dimensional Geometry
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
- Equation of a Line in Space
- Angle Between Two Lines
- Shortest Distance Between Two Lines
- Equation of a Plane in Normal Form
- Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point
- Equation of a Plane Passing Through Three Non Collinear Points
- Intercept Form of the Equation of a Plane
- Plane Passing Through the Intersection of Two Given Planes
- Coplanarity of Two Lines
- Angle Between Two Planes
- Distance of a Point from a Plane
- Angle Between Line and a Plane
- Vector and Cartesian Equation of a Plane
- Vector and Cartesian Equations of a Line
Linear Programming
Probability
- Introduction of Probability
- Conditional Probability
- Properties of Conditional Probability
- Multiplication Theorem on Probability
- Bayes’ Theorem
- Random Variables and Its Probability Distributions
- Mean of a Random Variable
- Variance of a Random Variable
- Bernoulli Trials and Binomial Distribution
- Independent Events
description
- Introduction of Inverse Trigonometric Functions
notes
As we studied in the last chapter, Functions is a special relation in which no two distinct ordered pairs have same first element i.e if y=f(x), then for one value of x we cannot have two values of y.
Also we studied that trignometric ratios behave like trignometric functions. A function must be invertible for finding it's Inverse. In this chapter, we shall study about the restrictions on domains and ranges of trigonometric functions which ensure the existence of their inverses and observe their behaviour through graphical representations.
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