Basic Fundamentals

Duration: 17 min

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Module outline

  1. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive introduction to the basics of trigonometry. The lecture begins by defining trigonometry as the measurement of three sides of a triangle. It then introduces the fundamental concept of trigonometric ratios using a right-angled triangle, labeling the sides as perpendicular (P), base (B), and hypotenuse (H), and defining the ratios for sine (sin), cosine (cos), and tangent (tan) as P/H, B/H, and P/B respectively. The video also covers the reciprocal ratios: cosecant (cosec), secant (sec), and cotangent (cot), which are the inverses of sin, cos, and tan. A key part of the lesson is the presentation of a table of trigonometric values for standard angles (0°, 30°, 45°, 60°, 90°), including sin, cos, tan, cot, sec, and cosec. The video concludes by introducing the three primary trigonometric identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ, and explains how these ratios are used to define trigonometric functions for any angle.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide displaying 'TRIGONOMETRY' in yellow text. The instructor then begins the lesson by writing 'Basics of Trigonometry :' on the screen. He explains that trigonometry is the measurement of the three sides of a triangle, which is visually represented by drawing three horizontal lines to symbolize the three sides.

  2. 2:00 – 5:00 02:00-05:00

    The instructor draws a right-angled triangle and labels its sides: perpendicular (P), base (B), and hypotenuse (H). He then introduces the three primary trigonometric ratios: sinθ = P/H, cosθ = B/H, and tanθ = P/B. He writes these formulas on the screen and explains that these ratios are derived from the sides of the triangle.

  3. 5:00 – 10:00 05:00-10:00

    The video continues by introducing the reciprocal trigonometric ratios. The instructor writes the formulas for cosecθ = 1/sinθ = H/P, secθ = 1/cosθ = H/B, and cotθ = 1/tanθ = B/P. He also shows the relationships between the ratios, such as tanθ = sinθ/cosθ and cotθ = cosθ/sinθ, which are written in a box on the screen.

  4. 10:00 – 15:00 10:00-15:00

    A table titled 'Values at angles' is displayed, showing the values of sinθ, cosθ, tanθ, cotθ, secθ, and cosecθ for the standard angles 0°, 30°, 45°, 60°, and 90°. The instructor fills in the table step-by-step, starting with sinθ and cosθ, and then calculating the other ratios based on the values of sin and cos.

  5. 15:00 – 17:07 15:00-17:07

    The instructor introduces the three fundamental trigonometric identities: (1) sin²θ + cos²θ = 1, (2) 1 + tan²θ = sec²θ, and (3) 1 + cot²θ = cosec²θ. He explains that these identities are derived from the Pythagorean theorem and are used to relate the trigonometric ratios. The video concludes by showing how these ratios are used to define trigonometric functions for any angle.

The video provides a structured and logical progression of the fundamentals of trigonometry. It starts with the definition and core concept of measuring a triangle's sides, then builds upon this by introducing the six trigonometric ratios using a right-angled triangle as a visual aid. The lesson is reinforced with a detailed table of values for standard angles, which is essential for problem-solving. The final segment on trigonometric identities ties the concepts together, showing the relationships between the ratios and their applications. This comprehensive approach ensures a solid foundation for understanding trigonometric functions.

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