Domain and Range of Trigonometric Functions

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Topics

  • Angle and Its Measurement
    • Directed Angle
    • Angles of Different Measurements
    • Angles in Standard Position
    • Measures of Angles
    • Area of a Sector of a Circle
    • Length of an Arc of a Circle
  • Trigonometry - 1
    • Introduction of Trigonometry
    • Trigonometric Functions with the Help of a Circle
    • Signs of Trigonometric Functions in Different Quadrants
    • Range of Cosθ and Sinθ
    • Trigonometric Functions of Specific Angles
    • Trigonometric Functions of Negative Angles
    • Fundamental Identities
    • Periodicity of Trigonometric Functions
    • Domain and Range of Trigonometric Functions
    • Graphs of Trigonometric Functions
    • Polar Co-ordinate System
  • Trigonometry - 2
    • Trigonometric Functions of Sum and Difference of Angles
    • Trigonometric Functions of Allied Angels
    • Trigonometric Functions of Multiple Angles
    • Trigonometric Functions of Double Angles
    • Trigonometric Functions of Triple Angle
    • Factorization Formulae
    • Formulae for Conversion of Sum Or Difference into Product
    • Formulae for Conversion of Product in to Sum Or Difference
    • Trigonometric Functions of Angles of a Triangle
  • Determinants and Matrices
  • Straight Line
    • Locus of a Points in a Co-ordinate Plane
    • Straight Lines
    • Equations of Line in Different Forms
    • General Form of Equation of a Line
    • Family of Lines
  • Circle
  • Conic Sections
    • Double Cone
    • Conic Sections
    • Parabola
    • Ellipse
    • Hyperbola
  • Measures of Dispersion
    • Meaning and Definition of Dispersion
    • Measures of Dispersion
    • Range of Data
    • Variance
    • Standard Deviation
    • Change of Origin and Scale of Variance and Standard Deviation
    • Standard Deviation for Combined Data
    • Coefficient of Variation
  • Probability
  • Complex Numbers
  • Sequences and Series
  • Permutations and Combination
    • Fundamental Principles of Counting
    • Invariance Principle
    • Factorial Notation
    • Permutations
    • Permutations When All Objects Are Distinct
    • Permutations When Repetitions Are Allowed
    • Permutations When Some Objects Are Identical
    • Circular Permutations
    • Properties of Permutations
    • Combination
    • Properties of Combinations
  • Methods of Induction and Binomial Theorem
    • Principle of Mathematical Induction
    • Binomial Theorem for Positive Integral Index
    • General Term in Expansion of (a + b)n
    • Middle term(s) in the expansion of (a + b)n
    • Binomial Theorem for Negative Index Or Fraction
    • Binomial Coefficients
  • Sets and Relations
  • Functions
  • Limits
    • Concept of Limits
    • Factorization Method
    • Rationalization Method
    • Limits of Trigonometric Functions
    • Substitution Method
    • Limits of Exponential and Logarithmic Functions
    • Limit at Infinity
  • Continuity
    • Continuous and Discontinuous Functions
  • Differentiation
    • Definition of Derivative and Differentiability
    • Rules of Differentiation (Without Proof)
    • Derivative of Algebraic Functions
    • Derivatives of Trigonometric Functions
    • Derivative of Logarithmic Functions
    • Derivatives of Exponential Functions
    • L' Hospital'S Theorem
  • Domain and Range of Trignometric Functions and Their Graphs

Notes

Domain is the set of all those values at which a function is defined.
1) sin x- 
Domain- R 
Range- [-1,1]

2) cos x- 
Domain- R
Range- [-1,1]

3) tan x-
Domain- `"R"- {x:x= (2n+1)π/2,  n∈ "Z"}`
Range- `"R"`

4) cot x-
Domain- `"R"- {x:x= nπ, n∈ "Z"}`
Range- `"R"`

5) sec x-
Domain- `"R"- {x:x= (2n+1) π/2, n∈ "Z"}`
Range- `"R"- (-1,1)`

6) cosec x- 
Domain- `"R"- {x:x= nπ, n∈ "Z"}`
Range- `"R"- (-1,1)`

 

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