Browse Formulas by Category
Equations and inequalities are at the heart of mathematics, providing tools to model relationships, solve problems, and understand patterns. From linear equations to advanced trigonometric inequalities, this page is a comprehensive resource for mastering all types of equations and their transformations. Whether you're a student, teacher, or professional, these formulas will help you solve problems with confidence and ease.
Linear Equation
Learn linear equation formulas, solution methods, and graphing techniques. Perfect for algebra and school exam preparation.
System of Two Linear Equation
Explore methods to solve systems of two linear equations: substitution, elimination, and matrix approaches. Ideal for algebra and coordinate geometry.
Quadratic Equation
Master quadratic equation formulas, roots via the quadratic formula, and discriminant analysis. Essential for algebra learners.
Exponential Equation
Understand exponential equation formulas and solve problems involving growth and decay models. Important for math and science.
Logarithmic Equation
Learn how to solve logarithmic equations using logarithm laws and base conversions. Applicable in algebra and calculus.
Trigonometric Equation Cos
Explore equations involving cos(x), how to solve them using identities and inverse functions. Key for trigonometry practice.
Trigonometric Equation Sin
Solve sin(x) equations using identities and inverse sine. Ideal for algebra and trigonometry studies.
Trigonometric Equation Tan
Learn to solve tan(x) equations with identities and periodicity rules. Useful in trigonometric problem solving.
Trigonometric Equation Cotan
Explore solutions to cot(x) equations using identities and reciprocal relations. Useful for advanced trigonometry.
Linear Inequation
Master solving linear inequations with interval notation and graphing methods. Ideal for algebra exam prep.
Quadratic Inequation
Learn techniques for solving quadratic inequalities using sign charts and critical points. Useful for algebra.
- Key Formula - General Forms
- General Form and Terminology
- Solution Cases
- Quadratic Formula (for finding roots)
- Applications
- Sign Analysis Method - Core Strategy
- Parabola Direction and Solution Patterns
- Discriminant Cases and Solution Types
- Solution Representation Methods
- Special Cases and Boundary Conditions
- Graphical Method and Verification
Exponential Inequation
Understand how to solve inequalities involving exponential expressions and their properties. Key for algebra and calculus.
Logarithmic Inequation
Discover methods to handle inequalities involving logarithms using log rules and domain considerations.
Trigonometric Inequation Cos
Solve cosine-based inequalities using identities and interval reasoning. Important for advanced trigonometry.
Trigonometric Inequation Sin
Handle inequalities involving sin(x) using domain and identity rules. Ideal for trigonometry problem-solving.
- Key Formula - General Form
- Key Inequality Analysis from Screenshot
- Case Analysis from Screenshot
- Unit Circle Analysis Method
- Sine Wave Analysis Method
- Standard Sine Inequality Solutions
- Special Case Solutions
- Composite Sine Inequalities
- Symmetry and Reference Angles
- Solution Verification and Domain
- Complete Case Analysis for sin x β₯ m
Trigonometric Inequation Tan
Learn how to solve tan(x) inequalities using periodicity and sign chart methods. Useful for trigonometry.
- Key Formula - General Form
- Key Inequality Analysis from Screenshot
- Key Information from Screenshot
- Unit Circle Analysis Method
- Tangent Wave Analysis Method
- Standard Tangent Inequality Solutions
- Special Case Solutions
- Asymptote Behavior Analysis
- Composite Tangent Inequalities
- Domain Restrictions and Asymptotes
- Complete Solution Analysis for tan x β₯ m
Trigonometric Inequation Cotan
Explore solving cot(x) inequalities using reciprocal relationships and periodic intervals.
- Key Formula - General Form
- Key Inequality Analysis from Screenshot
- Key Information from Screenshot
- Unit Circle Analysis Method
- Cotangent Wave Analysis Method
- Standard Cotangent Inequality Solutions
- Special Case Solutions
- Asymptote Behavior Analysis
- Composite Cotangent Inequalities
- Domain Restrictions and Asymptotes
- Complete Solution Analysis for cot x β₯ m
Constant
Learn about constant equations and their trivial solutions. Understand graph behavior and properties of constant functions.
Absolute
Master solving absolute value equations and understanding their piecewise behavior. Essential for algebra and graphing.
Square Root
Explore how to solve equations involving square roots and radicals. Learn domain checks and algebraic manipulation.
Parabolic
Understand parabolic equations in vertex and standard forms, graph features like axis and vertex location.
Cubic
Learn cubic equation formulas including roots finding and curve behavior. Advanced algebra topic for analysis.
Reciprocal
Explore reciprocal equations and properties of inverse functions. Useful in algebra and math models.
Sec
Solve equations involving sec(x) using reciprocal and identity-based approaches. Essential for advanced trigonometry.
Cosec
Discover solving cosec(x) equations using reciprocal relationships and trigonometric identities.
Horizontal Shifting
Learn horizontal shifting transformations of functions, how to translate graphs left or right. Key concept in function analysis.
Vertical Shifting
Understand vertical shifting in functions, translating graphs up or down. Important for graph analysis and transformations.
Reflection
Explore reflection transformations that mirror function graphs across the xβaxis or yβaxis. Useful in graphing techniques.
streching
Learn vertical and horizontal stretching transformations of function graphs. Key for understanding scaling behavior.
Why Choose Our Math Formula Collection?
β Comprehensive Coverage
Over 400 formulas across all major mathematical disciplines
π Solved Examples
Each formula includes detailed examples and step-by-step solutions
π― Easy Navigation
Well-organized categories for quick formula discovery
π Always Free
Complete access to all formulas without any restrictions
Never Struggle with Math Formulas Again!
Whether you're preparing for an exam, solving real-world problems, or just brushing up on your skills, our formula collection is designed to make learning math intuitive and efficient.
π Bookmark This PageEssential Equation Solving Concepts
βοΈ Equation Balance
Master the fundamental principle that whatever you do to one side, you must do to the other side.
π Solution Verification
Learn to check solutions by substitution and identify extraneous solutions in radical equations.
π Graphical Analysis
Understand how equations relate to graphs and use visual methods to find solutions and intersections.
π― Method Selection
Choose the most efficient solving method based on equation type, complexity, and desired solution form.
Equation Solving Tips
Identify Equation Type
Recognize whether you're dealing with linear, quadratic, exponential, or trigonometric equations first.
Isolate Variables Systematically
Use inverse operations in logical order to isolate the variable while maintaining equation balance.
Check Your Solutions
Always substitute solutions back into the original equation to verify correctness and catch errors.
Use Multiple Methods
Try different solving approaches (algebraic, graphical, numerical) to confirm solutions and gain insight.
Real-World Applications
Finance & Economics
Solve compound interest problems, optimize investment strategies, model economic growth, and calculate loan payments.
Science & Research
Model population dynamics, analyze chemical reactions, study radioactive decay, and solve physics problems.
Engineering & Technology
Design control systems, analyze signal processing, optimize manufacturing processes, and solve technical problems.
Data Analysis & Modeling
Create mathematical models, perform regression analysis, forecast trends, and analyze statistical relationships.
Quick Reference Guide
Equations and inequalities are at the heart of mathematics, providing tools to model relationships, solve problems, and understand patterns. From linear equations to advanced trigonometric inequalities, this comprehensive resource helps you master all types of equations and their transformations. Whether you're studying, teaching, or working on advanced projects, these formulas provide the foundation for mathematical problem-solving and real-world applications.