Concept To Remember
- P N Junction Basics
- Magnetic Field For A Straight Conductor And Amperes Law
- Magnetization And Application Of Amperes Law
- Magnetization Magnetism And Matter
- Magnetostatics Introduction And Biot Savart Law
- Galilean Laws Kepler Laws Centripetal Forces Gravitation
- Haloakanes And Haloarenes
- Capacitive Circuits Alternating Currents
- Faradays Law Of Induction Induced Emf
- Matrices
- Matrix And Determinant
- Gausss Law In Electrostatics
- Wave Nature Of Matter
- Laws Of Motion Newtons Second And Third Laws Of Motion
- Laws Of Motion Newtons First Law Of Motion
- Maxwells Equations And Electromagnetic Waves
- Lc Oscillations
- Lcr Circuit Applications
- Lcr Circuit Graphical Solution Alternating Currents
- Lcr Circuit Power Factor
- Lcr Circuits Analytical Solution Resonance
- Refraction At Spherical Surfaces And
- Refraction Through A Prism And Dispersion Ray Optics And Optical Instruments
- Relations And Functions
- Self Inductance And Energy In Magnetic Field Electromagnetic Induction
- Generalization Of Amperes Law And Its Applications
- Sequence Series
- Series And Parallel Combinations Of Cells Current And Electricity
- Permutation Combination
- Determinants
- What Is Light
- The Atomic Nucleus Fission And Radioactivity
- The Atomic Nucleus Masses And Stability
- The F And D Block Elements
- Wheatstones Bridge Meter Bridge And Potentiometer
- Chemical Bonds
- Chemical Equillibrium
- Chemical Kinetics
- Chemical Thermodynamics
- Chemistry Of Group 2 Element
- Chemistry Of Main Group Elements
- Chemistry Of P Block Elements
- Phenols
- Photoelectric Effect Einsteins Explanation
- Photoelectric Effects Facts And Prospects
- Three Dimensional Geometry
- Microscopes And Telescopes Ray Optics And Optical Instruments
- Tidal Forces Energy Conservation
- Field And Potential In P N Junction
- Field Due To Dipole And Continuous Charge Distributions
- Viewing Objects Eyes As An Optical Instrument Ray Optics And Optical Instruments
- Differential Equations
- Diffraction
- Dimensions Of Physical Quantities Dimensional Analysis And Its Applications
- Limits
- Linear Inequality In Two Variables
- Linear Inequality
- Linear Programming Problems
- Kinetic Theory Of Gases Equation Of Ideal Gas
- Biomolecules
- First Law Work Done In Different Thermodynamic Processes
- Nitrogen Containing Organic Compounds
- Planar Motion Motion In A Plane
- Alcohols
- Electric Current And Current Density
- Electrical Energy And Power
- Electrochemistry
- Electromagnetic Induction Electromagnetic Induction
- Electromotive Force And Ohms Law Current And Electricity
- Indefinite Integral
- Energy Stored In Capacitors Field In Dielectrics Gausss Law In Dielectrics
- Infinite Series
- Introduction To Kinematics Basic Mathematical Concepts
- Introduction To Thermodynamics First Law And Internal Energy
- Introduction To Waves Equation Sinusoidal And Speed Of Waves
- Inverse Trigonometric Functions
- Mobility And Temperature Dependence Of Resistivity Current And Electricity
- Modern Physics
- Logarithm
- Bohr Model Of Atom I
- Moment Of Inertia And Theorems Of Perpendicular And Parallel Axes
- Conductors Semiconductors And Insulators
- Ionic Equillibrium
- Conservation Laws Fundamental Forces Estimation Of Distances
- Continuity Differentiability And Application Of Derivatives
- Coordinate Compounds
- Doping In Semiconductors
- Force And Torque Due To Magnetic Field
- Forces On Bodies Contact And Non Contact Forces
- Forces On Bodies Systems Involving Strings Or Springs
- More Applications Of Amperes Law
- Work And Energy Basic Concepts Related To Constant And Variable Forces Kinetic Energy
- Work Energy And Impulse Momentum Principles Conservation Of Momentum
- Work Energy And Power Example Problems
- Torque And Angular Momentum System Of Particles And Rotational Motion
- Rotational Motion About A Fixed Axis Angular Momentum System Of Particles And Rotational Motion
- Motion Of Charges In The Presence Of Electric And Magnetic Fields
- Power Of A Lens And Combination Of Thin Lenses In Contact
- Optics Fringe Shift In The Two Hole Interference Equipment
- Optics Interference With Coherent And Incoherent Waves
- Optics Polarisation Of Light
- Optics Wave Optics Huygens Principle
- Optics Youngs Interference Experiment
- Equivalent Circuits
- Transformers
- Organic Chemistry Some Basic Principles And Techniques
- Drift Velocity And Resistance
- Trigonometric Functions
- Probability
- Problem Solving In Quantum Physics Of Atoms
- Problem Solving Modern Physics
- Problem Solving Session Structure Of Atom B
- Problems In Electromagnetics Electrostatics
- Problems In Electromagnetics Magnetic Fields Em Waves
- Problems In Kinematics Motion In A Plane
- Statistics
- Ethers
- Straight Lines
- Quadratic Equations
- Current Through A P N Junction
- Rutherford Scattering And Introduction To Bohr Model
- Hydrocarbons
- System Of Linear Equations
- Aldehydes Ketones Carboxylic Acids
- Arithmetic Geometric Harmonic Progressions
- Binomial Expansions
- Binomial Theorem
- Circles
- Circuits With Resistance And Inductance
- Complex Numbers
- Conic Sections
- Definite Integral
- Diffraction Patterns Due To A Single Slit And A Circular Aperture
- Entropy And T S Diagram
- Faradays Law Of Induction Mutual And Self Inductance
- Keplers Laws Centripetal Forces Galilean Law The Gravitational Law
- Kirchhoffs Laws Current And Electricity
- Moving Coil Galvanometer Ammeter And Voltmeter Potential Energy Of A Dipole
- Set Theory
- Vectors
- Ac Current Generator
- Accuracy And Precision Of Measuring Instruments
- Animal Kingdom Part
- Application Of Biotechnology In Agriculture
- Application Of Biotechnology In Medicine
- Applications Of Gausss Law
- Atomic Models
- Biology In Human Welfare Human Health And Disease
- Biology In Human Welfare Human Health And Disease
- Biology In Human Welfare Microbes In Human Welfare
- Biotechnology And Its Application Part
- Biotechnology Principles And Processes Part
- Carnot Engine And Carnot Theorem
- Cell Structure And Function Biomolecules
- Cell Structure And Function Cell Cycle And Cell Division
- Cell Structure And Function Cell The Unit Of Life
- Concept Of Charge And Coulombs Law
- Concept Of Waves And Electromagnetic Waves
- Cylindrical And Spherical Capacitors Series And Parallel Combinations
- Determination Of Gravitational Constant G
- Diamagneticparamagnetic And Ferromagnetic Materialsmagnetic Field Of The Earth
- Displacement Current
- Ecology Biodiversity And Conservation
- Ecology Ecosystems (Ecology And Environment)
- Ecology Organisms And Populations(Diversity Of Living Organisms)
- Electric Field And Potential And Concept Of Capacitance
- Electrostatic Potential And Potential Energy
- Equilibrium Of A Rigid Body Moments And Center Of Gravity
- Equipartiton Of Energy
- Examples Of Simple Harmonic Motion
- Forces On Bodies Procedure To Solve Problems
- Forces On Bodiesproblems Involving Multiple Bodies
- Frame Of Reference Motion In A Straight Line Uniform
- Genetics And Evolution Concepts Summary And Evolution
- Genetics And Evolution Evolution
- Genetics And Evolution Molecular Basis Of Inheritance
- Genetics And Evolution Principles Of Inheritance And Variation
- Gravitation
- Heat Engine And Refrigerators
- Human Physiology Body Fluids And Circulation
- Human Physiology Breathing And Exchange Of Gases
- Human Physiology Chemical Coordination And Integration
- Human Physiology Excretory Products And Their Elimination
- Human Physiology Locomotion And Movement
- Human Physiology Neural Control And Coordination
- Impact And Collision
- Integral Calculus
- Introduction To Periodic Motion
- Introduction To Simple Harmonic Motion
- Introduction To Vector Operations
- Introduction To Vectors
- Introduction To Wavesequationsinusoidal And Speed Of Waves
- Introductioncenter Of Masssystem Of Particles And Rotational Motion
- Matter Waves Structure Of The Atom
- Mean Freepath And Non Ideal Gas
- Measurements And Introduction To Error Analysis
- Mechanical Properties Of Fluids
- Mechanical Properties Of Solids
- Microscopic And Macroscopic Approach To Thermal Properties
- Motion In A Straight Line
- Motion Of Center Of Mass Relative Motion And Reduced Mass
- Natural And Artificial Satellites
- Opticsgeneral Introduction
- Opticsreflection Of Light And Formation Of Images
- Photosynthesis And Respiration Respiration
- Plant Growth And Development
- Plant Physiology Photosynthesis
- Potential And Potential Energy
- Potential Due To Different Charge Distributions
- Problem Of Matrices
- Problem On Quadratic Equations
- Problem Sessionmotion Of System Of Particles And Rigid Bodies
- Problem Solving Electrostatics
- Problem Solving Law Of Motion
- Problem Solving Newtons Second Law
- Problem Solving Session Aldehydes And Ketones
- Problem Solving Simple Harmonic Motion
- Problems On Trig And Inv Trig Functions
- Redox Reactions
- Reflection Of Waves Superposition Of Waves Standing Waves On A String And Their Frequencies
- Refraction Of Lightray Optics And Optical Instruments
- Reproduction Human Reproduction
- Reproduction Sexual Reproduction In Flowering Plants
- Rotational Motion About A Fixed Axis Kinematics And Dynamics
- Series And Parallel Combination Of Resistances
- Simple Experiments Based On Basic Principles Of Mechanics
- Solution
- Standing Waves In A Pipe Phenomena Of Beats And Doppler Effect
- Structural Organization Anatomy Of Flowering Plants
- Structural Organization Morphology Of Plants
- Structural Organization Structural Organization In Animals
- Superposition Principle For Electrostatic Force
- The Atomic Nucleus
- The Concept Of Electric Field
- The Mirror Equationray Optics And Optical Instruments
- The Structure Of The Atom
- Thermal Properties Of Matter
- Total Internal Reflectionray Optics And Optical Instruments
- Units Of Measurementsystems Of Unitssi Unitsfundamental
- Vector Products Angular Velocity And Angular Acceleration
- Work Energy Theorem And Concept Of Potential Energy
Inverse Trigonometric Functions
Inverse Trigonometric Functions
Concept: Definition
Inverse trigonometric functions are functions that undo the trigonometric functions.
Concept: Notation
The inverse trigonometric functions are denoted by:
sin^(-1)(x)cos^(-1)(x)tan^(-1)(x)cot^(-1)(x)sec^(-1)(x)csc^(-1)(x)
Concept: Domain and Range
| Function | Domain | Range |
|---|---|---|
sin^(-1)(x) | [-1, 1] | [-π/2, π/2] |
cos^(-1)(x) | [-1, 1] | [0, π] |
tan^(-1)(x) | All real numbers | (-π/2, π/2) |
cot^(-1)(x) | All real numbers except 0 | (0, π) |
sec^(-1)(x) | (-∞, -1] ∪ [1, ∞) | [0, π/2) ∪ (π/2, π] |
csc^(-1)(x) | (-∞, -1] ∪ [1, ∞) | [-π/2, 0) ∪ (0, π/2] |
Concept: Graphs
sin^(-1)(x):
- Starts at (-1, -π/2)
- Ends at (1, π/2)
cos^(-1)(x):
- Starts at (-1, π)
- Ends at (1, 0)
tan^(-1)(x):
- Starts at (-∞, -π/2)
- Ends at (∞, π/2)
cot^(-1)(x):
- Starts at (-∞, 0)
- Ends at (∞, π)
sec^(-1)(x):
- Starts at (-∞, π/2)
- Ends at (-1, π)
- Starts again at (1, 0)
- Ends at (∞, π/2)
csc^(-1)(x):
- Starts at (-∞, -π/2)
- Ends at (-1, 0)
- Starts again at (1, π/2)
- Ends at (∞, π/2)
Concept: Identities
sin^(-1)(x) = cos^(-1)√(1 - x^2)cos^(-1)(x) = sin^(-1)√(1 - x^2)tan^(-1)(x) = cot^(-1)(1/x)cot^(-1)(x) = tan^(-1)(1/x)sec^(-1)(x) = cos^(-1)(1/x)csc^(-1)(x) = sin^(-1)(1/x)
Concept: Applications
Inverse trigonometric functions are used in a variety of applications, including:
- Solving trigonometric equations
- Finding the angle between two lines
- Finding the area of a triangle
- Finding the direction of a vector
BETA
