Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivatives of Inverse Functions
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
- Indefinite Integration with Standard Indefinite Integral Formulae
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Methods of Integration> Integration Using Partial Fraction
- Overview of Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Homogeneous Differential Equations
- Linear Differential Equations
- Applications of Differential Equation
- Solution of a Differential Equation
- Overview of Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
- Bernoulli Trial
- Mean and Variance of Binomial Distribution
- Probability using Binomial Distribution
- Overview of Binomial Distribution
Estimated time: 6 minutes
Maharashtra State Board: Class 12
Key Points: Domain and Range of Inverse Trigonometric Functions
| Function | Domain | Range (Principal Value) |
|---|---|---|
| sin⁻¹x | −1 ≤ x ≤ 1 | −π/2 ≤ y ≤ π/2 |
| cos⁻¹x | −1 ≤ x ≤ 1 | 0 ≤ y ≤ π |
| tan⁻¹x | (−∞, ∞) | −π/2 < y < π/2 |
| cosec⁻¹x | (−∞, −1] ∪ [1, ∞) | −π/2 ≤ y ≤ π/2, y ≠ 0 |
| sec⁻¹x | (−∞, −1] ∪ [1, ∞) | 0 ≤ y ≤ π, y ≠ π/2 |
| cot⁻¹x | (−∞, ∞) | 0 < y < π |
Maharashtra State Board: Class 12
Formula: Inverse Trigonometric Function
Direct Identities
- sin⁻¹(sin θ) = θ, if −π/2 ≤ θ ≤ π/2
- cos⁻¹(cos θ) = θ, if 0 ≤ θ ≤ π
- tan⁻¹(tan θ) = θ, if −π/2 < θ < π/2
Inverse Identities
- sin(sin⁻¹x) = x, if −1 ≤ x ≤ 1
- cos(cos⁻¹x) = x, if −1 ≤ x ≤ 1
- tan(tan⁻¹x) = x, for all real x
Other Important Ones
- sec⁻¹(sec θ) = θ, if 0 ≤ θ ≤ π, θ ≠ π/2
- cosec⁻¹(cosec θ) = θ, if −π/2 ≤ θ ≤ π/2, θ ≠ 0
- cot⁻¹(cot θ) = θ, if 0 < θ < π
Video Tutorials
Shaalaa.com | Inverse Trigonometry Functions part 2 (Natural domain Range)
to track your progress
