Trigonometry function

Fundamental Concepts

• Mathematics is a formal system of logic and reasoning used to quantify, order, and understand the world.
• It encompasses various branches, including arithmetic, algebra, calculus, geometry, and more.
• Key mathematical tools include numbers, symbols, and operations.
• Mathematics is crucial for problem-solving in diverse fields, from science and engineering to finance and economics.
• Mathematical concepts are often presented in a structured and abstract language.

Number Systems

• Natural numbers (counting numbers): 1, 2, 3, ...
• Whole numbers: 0, 1, 2, 3, ...
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
• Rational numbers: numbers that can be expressed as a fraction p/q where p and q are integers and q is not zero.
• Irrational numbers: numbers that cannot be expressed as a fraction of two integers. Examples include pi (π) and the square root of 2 (√2).
• Real numbers: the set of all rational and irrational numbers.
• Imaginary numbers: numbers whose square is negative. Expressed as multiples of i where i² = -1.
• Complex numbers: the union of real and imaginary numbers in the form a + bi, where a and b are real numbers.

Arithmetic Operations

• Addition (+): Combining quantities.
• Subtraction (-): Finding the difference between quantities.
• Multiplication (× or *): Repeated addition.
• Division (÷ or /): Repeated subtraction or finding a quotient.
• Exponentiation (^): Repeated multiplication (e.g., 2^3 = 2 × 2 × 2).
• Order of operations (PEMDAS/BODMAS): a set of rules for evaluating expressions with multiple operations.

Algebra

• Variables: Symbols representing unknown values.
• Equations: Statements of equality between expressions.
• Solving equations: Finding the value(s) of the variable(s) that satisfy the equation.
• Inequalities: Statements comparing quantities using symbols like <, >, ≤, ≥.
• Polynomials: Expressions involving variables and coefficients.
• Factoring: Breaking down an expression into simpler expressions.
• Systems of equations: Multiple equations with multiple variables.

Geometry

• Shapes and their properties: Lines, angles, triangles, quadrilaterals, circles, and more.
• Measurement: Calculating lengths, areas, and volumes.
• Transformations: Translations, rotations, and reflections of shapes.
• Coordinate geometry: Using coordinates to locate points on a plane.
• Euclidean geometry: The study of geometry based on Euclid's postulates.

Calculus

• Limits: Approaching values of a function.
• Derivatives: instantaneous rate of change.
• Integrals: finding the area under a curve.
• Applications: Solving problems involving motion, growth, and optimization.

Statistics and Probability

• Data collection and analysis.
• Measures of central tendency (mean, median, mode).
• Measures of dispersion (variance, standard deviation).
• Data visualization (graphs, charts).
• Probability: Calculating the likelihood of events.
• Probability distributions: describing the probability of outcomes.

Logic and Reasoning

• Deductive reasoning: Moving from general truths to specific conclusions.
• Inductive reasoning: Moving from specific observations to general conclusions.
• Proof techniques: Strategies for validating mathematical statements.
• Sets and logic: Defining sets and relationships within sets, fundamental principles of logical deduction.