Razon
Search
Search
Dark mode
Light mode
Explorer
Astronomy
Horizontal Coordinate System
Orbital Mechanics
The Celestial Sphere
Units of Distance
Computer Science
Cryptography
Hash Functions
Birthday Attacks
Davies-Meyer Transform
Merkle-Damgård Transform
Security Definitions
Integrity Verification
Merkle Trees
Key Management
Key Exchange
Diffie-Hellman Key Exchange
Security Definitions
Primitives
Pseudorandom Function Generators (PRFGs)
Pseudorandom Generators (PRGs)
Pseudorandom Permutations (PRPs)
Private-Key Cryptography
Block Ciphers
Modes of Operation
Cipher Block Chaining (CBC) Mode
Counter (CTR) Mode
Electronic Cookbook (ECB) Mode
Advanced Encryption Standard (AES)
Encrypting Non-Conforming Messages
Padding Oracle Attack
Message Authentication Codes (MACs)
Fixed-Length MACs
Hash-Based MACs (HMAC)
Security Definitions
Ciphertext-Only Attack (COA)
Perfect Secrecy
Semantic Security
Chosen Ciphertext Attack (CCA)
Chosen Plaintext Attack (CPA)
Ciphertext Integrity (CI)
P vs NP
Stream Ciphers
Hardware-Oriented Stream Ciphers
Authenticated Encryption
One-Time Pad
One-Time Passwords
Public-Key Cryptography
Security Definitions
Chosen-Plaintext Attack (CPA)
Breaking Classical Cryptrography
Cybersecurity
Exploitation
Binary Exploitation
Heap Exploitation
Use After Free (UAF)
Stack Exploitation
Buffer Overflows
Format String Vulnerabilities
Protection Mechanisms
Return to _dl_resolve
Return-oriented programming (ROP)
Sigreturn-oriented Programming (SROP)
DNS
DNS Cache Poisoning
DNS Traffic Amplification
Web
SQL Injection
Database Enumeration
Union Injection
Command Injection
CRLF Injection
Cross-Site Request Forgery
Cross-Site Scripting (XSS)
Directory Traversal
File Inclusion
File Upload
Host Header Injection
HTTP Parameter Pollution
HTTP Response Splitting
Open Redirect
PHP Object Injection
Template Injection
Hardware Hacking
Wireless Attacks
Deauth Attack
Hacking WEP Networks
Hacking WPA Networks
Post Exploitation
Active Directory (AD)
Domain Data Enumeration with Bloodhound
Domain Enumeration with PowerView
Enumeration
Linux
Hunting Down Sensitive Files
Network Enumeration
System Enumeration
User Enumeration
Windows
System Enumeration
Pivoting
SSH Tunneling
Tunneling with Chisel
Privilege Escalation
Linux
Abusing Linux Capabilities
Abusing SUID & SGID Binaries
Kernel Exploits
NFS Root Squashing
Sudo Escalation via LD_PRELOAD
Sudo Shell Escape Sequences
Windows
Misconfigured Services
Insecure Service Executable Permissions
Insecure Service Permissions
Unquoted Service Paths
Weak Registry Permissions
AlwaysInstallElevated Group Policy
AutoRun Programmes
Bypassing UAC
Kernel Exploits
Scheduled Tasks
Startup Applications
Stored Credentials
Token Impersonation
Reconnaissance
Enumeration
Port Scanning
FIN, NULL & XMAS Scans
Operation Security (OpSec)
SYN Scan
TCP Connect Scan
Vulnerability Scanning
Nmap Scripting Engine (NSE)
DNS Server Enumeration (53)
FTP Enumeration (21)
LDAP Enumeration (389, 636, 3268, 3269)
SNMP Enumeration (161)
Web Server Enumeration (80, 443)
Open-Source Intelligence (OSINT)
Domain Name Enumeration
Google Dorks
Harvesting E-Mails
Subdomain Enumeration
Whois Enumeration
Reverse Engineering
Assembly Programming
x86-64
Addressing Modes
Data Representation
Instruction Set
Memory
Registers
Variables
Binary Formats
ELF
Dynamic Linking
Relocations
Sections
Segments
Symbols
The ELF Header
PE
NT Headers
Relocations
Sections
The DOS Header
The DOS Stub
The Rich Header
Program Anatomy
Registers
The Heap
The Stack
Assembly
Networking
Application Layer Addressing
Uniform Resource Locators (URLs)
URL Encoding
Protocols
Address Resolution Protocol (ARP)
Address Resolution
ARP Caching
ARP Message Format
ARP Proxying
Reverse Address Resolution (RARP)
Domain Name System (DNS)
The Domain Name System
The in-addr.arpa Domain
Hypertext Transfer Protocol (HTTP)
HTTP Requests
HTTP Methods
Internet Protocol (IP)
Internet Protocol v4 (IPv4)
Classful Addressing
Classless Inter-Domain Routing (CIDR)
IPv4 Datagrams
Subnetting
WLAN (IEEE 802.11)
Management Frames
Association Frames
Authentication Frames
Discovery Frames
Authentication and Association
Encryption and Integrity
WiFi Protected Access (WPA)
Ethernet
File Transfer Protocol (FTP)
Leightweight Directory Access Protocol (LDAP)
Network Time Protocol (NTP)
Server Message Block (SMB)
Simple Network Management Protocol (SNMP)
The TCP-IP Suite and the OSI Model
(1) The Physical Layer
(2) The Datalink Layer
Subnetting
VLANs
System Internals
Linux
Command Line
File System
Windows
Active Directory (AD)
Schema
Default Schema
Computers
Contacts
Domain Controllers
Groups
Users
Attributes
Classes
Domain Controllers
Naming Contexts
The Active Directory Hierarchy
The Directory Information Tree (DIT)
PowerShell
Commands
Commandlets
Execution Policies
PowerShell
PSDrives
Variables
File System
Theoretical Computer Science
Algorithm Efficiency
Negligible Function
Time Complexity
Economics
Languages
Bulgarian
Spelling
Spelling Adjectives
Spelling Adverbs
Spelling Nouns
Spelling Particles
Nouns
Orthography
The Definite Article
Latin
Cases
Ablative
Endings
Accusative
Endings
Dative
Endings
Genitive
Endings
Nominative
Endings Chart
Vocative
Endings
Adjectives
Nouns
Mathematics
Algebra
Algebraic Structures
Operations
Binary Operations
Closure
Operations
Unary Operations
Algebraic Structures
Equations
Differential Equations
Ordinary Differential Equations (ODEs)
Polynomial Equations
Real Polynomial Equations
Trigonometric Equations
Real Trigonometric Equations
Equations
Fields
Complex Numbers
Operations with Complex Numbers
The Real Numbers
Real Polynomials
Groups
Abelian Groups
Inequalities
Logarithmic Inequalities
Linear Algebra
Linear Transformations
Dual Spaces
Dual Space
Kernel
Linear Form
Linear Transformation
Matrix Representations of Linear Transformations
Properties of Linear Transformations
Matrices
Complex Matrices
Unitary Matrices
Orthonormal Bases from Unitary Matrices
Unitary Matrix
Complex Matrix
Hermitian Transposition
Matrix Operations
Matrix Addition
Matrix Product
Matrix Transposition
Scalar Multiplication
Real Matrices
Real Orthogonal Matrices
Length Preservation of Real Orthogonal Matrices
Orthonormal Bases from Orthogonal Matrices
Real Orthogonal Matrix
Real Symmetric Matrices
Definiteness of Real Symmetric Matrices
Real Symmetric Matrix
Real Matrix
Row and Column Vectors
Complex Vectors
Complex Dot Product
Complex Vector
Structure of the Complex Vector Space
Real Vectors
Canonical Norm in the Real Vector Space
Real Cross Product
Real Dot Product
Real Vector
Standard Basis of the Real Vector Space
Structure of the Real Vector Space
Column Vector
Row Vector
Standard Basis
Square Matrices
Determinants
Calculating the Determinant
Cofactor Matrix
Determinant
Effects of Row and Column Operations on Determinants
Diagonal Matrices
Diagonal Matrix
Inverting Diagonal Matrices
Eigentheory
Characteristic Polynomial
Eigenbasis
Eigendecomposition
Eigenspace
Eigenvalue
Eigenvector
Linear Independence of Eigenvectors
Invertibility
Finding Matrix Inverses
Invertibility
Orthogonal Matrices
Determinants of Orthogonal Matrices
Orthogonal Matrix
Product of Orthogonal Matrices
Symmetric Matrices
Symmetric Matrix
Identity Matrix
Matrix Similarity
Square Matrix
Trace
Triangular Matrices
Column Rank = Rank = Row Rank
Column Space
Matrix
Null Space
Row Space
Vector Space of Matrices
Zero Matrix
Systems of Linear Equations
Augmented Matrix
Coefficient Matrix
Elementary Row Operations
Gauss-Jordan Elimination
Homogeneous System of Linear Equations
Matrix Form of a System of Linear Equations
Rank
Row Echelon Form
Solvability of a System of Linear Equations
System of Linear Equations
Vector Spaces
Bases
Basis
Basis Criteria
Basis Representation
Coordinate Vector
Dimension
Ordered Basis
Steinitz Exchange Lemma
Inner Product Spaces
Angle
Canonical Norm
Euclidean Distance
Euclidean Metric
Gram-Schmidt Orthonormalisation Process
Inner Product Space
Orthogonal Basis
Orthogonal Complement
Orthogonality
Orthonormal Basis
Normed Vector Spaces
Norm
Normed Vector Space
Unit Vector
Complex Vector Space
Linear Combination
Linear Dependence
Linear Independence
Real Vector Space
Span
Spanning Set (Generator)
Subspace
Vector
Vector Space
Rings
Commutative Rings
Integral Domains
Euclidean Domains
Euclidean Domain
Euclidean Function
Integral Domain
Polynomials
Univariate Polynomials
Polynomial Division
Monomials
Quadratic Polynomials
Zero Polynomial
Zero Ring
Monoid
Analysis
Analysis on Manifolds
Coordinate Representation of Functions
Smooth Manifolds
Smoothness of Functions on Manifolds
Complex Analysis
Complex Functions
Complex Analytic Functions
Continuity
Continuity of Complex Functions
Limits
Evaluating Limits of Complex Functions
Infinite Limits of Complex Functions
Limits of Complex Functions
Boundedness of Complex Functions
Complex Functions
Exponentiation of Real Numbers
Periodicity of Complex Functions
The Complex Exponential Function
The Complex Natural Logarithm
Complex Power Series
Complex Power Series
Convergence of Complex Power Series
Complex Sequences
Boundedness of Complex Sequences
Complex Sequences
Convergence of Complex Sequences
Complex Series
Complex Series
Convergence of Complex Series
Complex-Valued Function
Topology of the Complex Plane
Functions
Injection, Surjection, Bijection
Bijection
Injection
Involution
Surjection
Sequences
Convergence of Sequences
Limit of a Sequence
Sequences
Composition
Functions
Identity Function
Restriction
Real Analysis
Real Functions
Differentiation
Critical Points
Derivatives of Elementary Functions
Differentiability of Real Functions
Differentiation Rules
Integration
Elementary Antiderivatives
Improper Integrals
The Fundamental Theorem of Real Analysis
Limits of Real Functions
Asymptotes of Real Functions
Limit Properties
Logarithms
Real Natural Function
Real Trigonometric Functions
Inverse Trigonometric Functions
Real Arccosine Function
Antiderivatives of the Real Arccosine Function
Continuity of the Real Arccosine Function
Derivative of the Real Arccosine Function
Real Arccosine Function
Real Arccotangent Function
Antiderivatives of the Real Arccotangent Function
Continuity of the Real Arccotangent Function
Derivative of the Real Arccotangent Function
Real Arccotangent Function
Real Arcsine Function
Antiderivatives of the Real Arcsine Function
Continuity of the Real Arcsine Function
Derivative of the Real Arcsine Function
Real Arcsine Function
Real Arctangent Function
Antiderivatives of the Real Arctangent Function
Continuity of the Real Arctangent Function
Derivative of the Real Arctangent Function
Real Arctangent Function
Real Inverse Trigonometric Functions
Real Cosine Function
Continuity of the Real Cosine Function
Derivative of the Real Cosine Function
Properties of the Cosine Function
Real Cosine Function
Real Cotangent Substitution
Continuity of the Real Cotangent Function
Derivative of the Real Cotangent Function
Properties of the Real Cotangent Function
Real Cotangent Function
Real Sine Function
Continuity of the Real Sine Function
Derivative of the Real Sine Function
Properties of the Real Sine Function
Real Sine Function
Real Tangent Function
Continuity of the Real Tangent Function
Derivative of the Real Tangent Function
Properties of the Real Tangent Function
Real Tangent Function
Trigonometric Identities
Composition of Trigonometric Functions and their Inverses
Fundamental Trigonometric Identities
Trigonometric Identities for Angle Products
Trigonometric Identities for Angle Sums
Trigonometric Identities for Argument Offsets
Trigonometric Identities for Function Products
Trigonometric Identities for Function Sums
Universal Trigonometric Substitution
Real Trigonometric Functions
Trigonometric Functions of Standard Angles
Continuity of Real Functions
Extrema
Monotony of Real Functions
Periodicity of Real Functions
Real Analytic Functions
Real Exponential Function
Real Functions
Real Functions
Real Functions
Real Power Series
Convergence of Real Power Series
Real Sequences
Convergence of Real Sequences
Monotony of Real Sequences
Real Series
Convergence of Real Series
Real Series
Real Vector Functions
Differentiation
Differentiability implies Continuity
Differentiability of Real Vector Functions
Differentiation Rules for Real Vector Functions
Jacobian Matrix
Partial Derivatives of Real Vector Functions
Smoothness of Real Vector Functions
Parametric Curves
Differentiation
Binormal Vector
Differentiability of Parametric Curves
Differentiation Rules for Curve Parameterisations
Normal Vector
Tangent Vector
Length of Parametric Curves
Limits of Parametric Curves
Orientation of Parametric Curves
Parametric Curve
Regularity of Parametric Curves
Parametric Surfaces
Equivalence of Parametric Surfaces
Parametric Surface
Smoothness of Parametric Surfaces
Surface Normal Vector
Scalar Fields
Differentiation
Differentiability of Real Scalar Fields
Differentiation Rules for Scalar Fields
Directional Derivatives of Real Scalar Fields
Gradient
Hessian Matrix
Partial Derivatives in Different Coordinate Systems
Partial Derivatives of Real Scalar Fields
Partial Differentiability of Real Scalar Fields
Symmetry of Second Derivatives
Extrema
Constraints
Critical Point
Global Extrema of Real Scalar Fields
Local Extrema
Method of Lagrange Multipliers
Saddle Point
Integration
Double Integral of a Real Scalar Field
Double Integrals
Double Riemann Sum
Line Integrals of Scalar Fields
Parametric Integrals
Scalar Surface Integral
Continuity of Real Scalar Fields
Limits of Real Scalar Fields
Real Scalar Field
Vector Fields
Conservative Vector Fields
Conservative Vector Field
Line Integrals of Conservative Vector Fields
Differentiation
Curl
Divergence
Integration
Definite Integrals of Vector Fields
Vector Line Integrals
Vector Surface Integral
Real Vector Field
Continuity of Real Vector Functions
Limits of Real Vector Functions
Linearity of the Limit Operator
Real Vector Function
Coordinate Systems
Euclidean Space
Real Analysis
Combinatorics
Combinations
Permutations
Variations
Formal Logic
Two-Valued Logic
Propositional Logic
Propositional Connectives
Propositional Logic
Propositional Logic
Propositional Logic
Truth Values
Two-Valued Logic
Formal Languages
Geometry
Euclidean Geometry
Angles
Plane Angles
Angle Bisector of a Plane Angle
Measure of a Plane Angle
Plane Angle
Curves
Straight Lines
Angle between Lines
Concurrent Lines
Line Segments
Parametric Equation of a Line
Straight Lines
Bounded Curve
Curvature
Curves
Rays
Euclidean Space
Coordinate Systems for Euclidean Space
Cartesian Coordinate System
Coordinate Transformations
Cylindrical Coordinate System
Polar Coordinate System
Spherical Coordinate System
Points in Geometry
Distance between Points
Length of a Vector
Half-Spaces
Planimetry
Plane Curves
Circles
Angles in a Circle
Chords in a Circle
Circles
Configurations of Lines and Circles
Polygons
Convex Polygons
Cyclic Polygon
Cyclic Polygons
Cyclic Polygon
Triangles
Cevians
Altitudes
Angle Bisectors
Cevians
Medians
Isosceles Triangles
Right Triangles
Right Triangles
Acute Triangle
Cyclicity of Triangles
Obtuse Triangle
Triangles
Perimeter
Tangential Polygons
Line Intersections in a Plane
Planimetry
Surfaces
Closed Surfaces
Closed Surfaces
Planes
Centroid
Congruence
Manifolds
Coordinate Systems
Atlas
Transition Maps
Closed Manifolds
Manifolds
Properties of Manifolds
General Regions in 2D
Probability Theory
Probability
Set Theory
Cardinality
Countable Sets
Size Comparisons for Sets
Collections
Operations with Collections
Ordering
Bounds
Intervals
Partial Order
Rays
Strict Partial Order
Strict Total Order
Total Order
Relations
Equivalence Relation
Reflexivity
Right-Unique Relation
Symmetry
Transitivity
Complement
Disjoint Sets
Index Sets
Multisets
Ordered Pairs
Power Set
Set Operations
Set Theory
Singletons
The Empty Set
Tuples
Statistics
Means
Topology
Bases for a Topological Space
Existence of a Topology with a Base
First-Countability Axiom
Neighbourhood Basis
Second-Countability Axiom
Subbase
Compactness
Local Compactness
Connectedness
Local Connectedness
Continuity
Homeomorphisms
Homeomorphic Spaces
Local Homeomorphisms
Locally Homeomorphic Spaces
Interior, Boundary, Exterior
Accumulation Points
Boundary
Closure
Denseness
Exterior
Interior
Isolated Points
Maps
Closed Map
Open Map
Metric Spaces
Boundedness in Metric Spaces
Continuity in Metric Spaces
Diameter of a Subset
Distance in Metric Spaces
Isometry
Metric Equivalence
Metrizable Space
Topological Spaces
Clopen Sets
Closed Sets
Neighborhoods
Open Sets
Hausdorff Spaces
Topological Subspaces
NavHub
Physics
Classical Mechanics
Frameworks for Classical Mechanics
Hamiltonian Formalism
Lagrangian Formalism
Newtonian Formalism
Space and Time
Electromagnetism
Electrostatics
Coulomb's Law
Permittivity
Vacuum Permittivity
Magnetostatics
Magnetic Field
Magnetic Force
Magnetic Permiability
Vacuum Magnetic Permiability
Charge Density
Electric Charge
Electric Flux
Gauss's Law
The Electric Field
Kinematics
Rotation
Angular Displacement
Translation
Translation with Constant Acceleration
Motion with Constant Acceleration
Motion with Constant Acceleration in 1D
Acceleration
Displacement
Path Length
Position
Velocity
Mechanics
Classical Mechanics
Fluid Mechanics
Fluid
Pascal's Law
Pressure in a fluid
Momentum
Conservation of Momentum
Impulse
Momentum
Momentum-Impulse Theorem
Newtonian Formalism
Collisions
Collision
Elastic Collision
Inelastic Collision
Perfectly Inelastic Collision
Energy
Conservation of Energy
Conservative Force
Kinetic Energy
Mechanical Energy
Potential Energy
Work
Work of a Constant Force
Newton's Laws of Translational Motion
Rest Mass
Rotation
Angular Momentum
Moment of Inertia
Torque
Classical Mechanics
Force in a Physical System
External Force
Internal Force
Relativistic Mechanics
Special Theory of Relativity
Minkowski Spacetime
Minkowski Metric
Minkowski Norm
Minkowski Spacetime
Length Contraction
Lorentz Boost
Lorentz Factor
Lorentz Transformation
Postulates of Special Relativity
Relativity of Event Order
Time Dilation
Vector Notation in Relativity
Force
Inertia
Mass
Pressure
Reference Frame
Speed of Light in a Vacuum
Physical Systems
Point Masses
Centre of Mass
Ideal Rigid Body
Point Mass
Closed System
Degree of Freedom
Microstate and Macrostate
Multiplicity
Parameter
Phase Space
Physical State
Physical System
Thermodynamics
Entropy
Entropy
Gases
Gases in Thermodynamic Processes
Ideal Gases in Adiabatic Processes
Ideal Gases in Isobaric Processes
Ideal Gases in Isohoric Processes
Ideal Gases in Isothermal Processes
Degrees of Freedom of Gas Particles
Entropy of an Ideal Gas
Ideal Gas Law
Internal Energy of an Ideal Gas
Kinetic-Molecular Model of an Ideal Gas
Molar Gas Constant
The Maxwell-Boltzmann Distribution
Work of an Ideal Gas
Heat Engines & Refrigerators
Carnot Engine
Carnot Refrigerator
Coefficient of Performance
Heat Engine
Refrigerator
Thermal Efficiency
Temperature and Heat
Heat Capacity
Molar Heat Capacity
Specific Heat Capacity
Temperature Change
Avogadro Constant
Boltzmann Constant
Coefficient of Volume Expansion
Heat
Heat Transfer
Internal Energy
Temperature
The First Law of Thermodynamics
Thermal Equilibrium
Thermal Expansion
Classical Reference Frame
Space and Time
Contributing
Usage
Home
❯
Mathematics
❯
Geometry
❯
Euclidean Geometry
❯
Angles
❯
Plane Angles
❯
Plane Angle
Plane Angle
Mar 04, 2025
1 min read
euclidean-geometry
geometry
mathematics
Definition: Plane Angle
TODO
Graph View
Backlinks
Angle Bisector of a Plane Angle
Angles in a Circle