Graphs, Domain and Range of Trig Func

Duration: 34 min

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Module outline

  1. About the course: About the Course
  2. Mathematical Aptitude: संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Divisibility Rules, प्रतिशत / Percentage, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय, चाल और दूरी / Time, Speed and Distance, Age Problems, मिश्रण और एलिगेशन / Mixture and Alligation, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Pipe and Cistern, Trigonometry, Statistics, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Logical Reasoning: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, सादृश्यता एवं वर्गीकरण / Analogy and Classification, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, क्रम एवं रैंकिंग / Order and Ranking, अशाब्दिक तर्क / Non-Verbal Reasoning, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, Syllogisms, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Analytical Reasoning (Counting Figures Reasoning), घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, कैलेंडर एवं घड़ी / Calendar and Clock, Clock
  4. General Knowledge: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Chemistry, Biology, History, Geography, Polity, Indian Economy, समसामयिकी / Current Affairs, Static General Knowledge
  5. Art of Teaching: शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन / Teaching-Learning Process and Classroom Management, Learners & Learning Process, Factors Affecting Teaching, शिक्षण विधियाँ एवं उपागम / Teaching Methods and Approaches, सूक्ष्म शिक्षण एवं कक्षा संप्रेषण / Microteaching and Classroom Communication, शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी / Teaching Aids and Educational Technology, आकलन एवं मूल्यांकन / Assessment and Evaluation, शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास / Teacher: Qualities, Professional Ethics and Development, शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन / Educational Policies, Acts and Administration, पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र / Curriculum, Arts and Co-curricular Areas, निर्देशन एवं परामर्श / Guidance and Counselling, दिव्यांग बच्चों की शिक्षा / Education of Children with Disabilities, Micro-Teaching & Teaching Skills, पाठ योजना / Lesson Planning
  6. Environmental Science: Environment
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | 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, Transaction Management, Concurrency Control
  14. Unit 7 | Computer Networks: Introduction to CN, Data Communication, 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
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js
  18. Unit 11 | 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
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, कंप्यूटर नेटवर्क / Computer Networks
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lecture on the domain, range, and graphs of the six primary trigonometric functions. The instructor begins by introducing the topic and then systematically analyzes each function: sine, cosine, tangent, cotangent, secant, and cosecant. For each function, the video displays its algebraic definition, constructs its graph on a Cartesian coordinate system, and explicitly states its domain and range. The graphs are drawn with key points and asymptotes, and the periodic nature of the functions is highlighted. The lecture also includes a table of standard trigonometric values and a final note summarizing that all trigonometric functions are periodic.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide: 'Domain, Range and Graph of Trigonometric functions :'. The first function, f(x) = sin x, is introduced. The instructor begins to set up a Cartesian coordinate system, drawing the x and y axes, and labels the x-axis with key angles in radians (π/2, π, 3π/2, 2π) and the y-axis with the value 1. The function is written as y = sin x.

  2. 2:00 – 5:00 02:00-05:00

    The instructor draws the graph of y = sin x, starting from the origin and creating a smooth, periodic wave. The graph is shown to pass through key points like (0,0), (π/2,1), (π,0), (3π/2,-1), and (2π,0). The instructor then labels the domain as (-∞, ∞) and the range as [-1, 1]. The periodicity is identified as 2π, with a visual arrow indicating the length of one period.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to the second function, f(x) = cos x. The instructor draws the graph of y = cos x, which is a sine wave shifted to the left by π/2. The graph is shown to pass through (0,1), (π/2,0), (π,-1), (3π/2,0), and (2π,1). The domain is stated as R (all real numbers), the range as [-1, 1], and the periodicity as 2π.

  4. 10:00 – 15:00 10:00-15:00

    The third function, f(x) = tan x, is introduced. The instructor writes the definition tan x = sin x / cos x and notes that cos x ≠ 0. The graph is drawn with vertical asymptotes at x = (2n+1)π/2, where n is an integer. The graph consists of repeating segments between the asymptotes, passing through the origin. The domain is given as R - {(2n+1)π/2}, the range as R, and the periodicity as π.

  5. 15:00 – 20:00 15:00-20:00

    The fourth function, f(x) = cot x, is presented. The definition cot x = cos x / sin x is written, with the condition sin x ≠ 0. The graph is drawn with vertical asymptotes at x = nπ, where n is an integer. The graph consists of repeating segments between the asymptotes, passing through the origin. The domain is R - {nπ}, the range is R, and the periodicity is π.

  6. 20:00 – 25:00 20:00-25:00

    The fifth function, f(x) = cosec x, is introduced with the definition cosec x = 1 / sin x, where sin x ≠ 0. The graph is drawn with vertical asymptotes at x = nπ. The graph consists of U-shaped curves above and below the x-axis, with peaks at y=1 and troughs at y=-1. The domain is R - {nπ}, the range is (-∞, -1] ∪ [1, ∞), and the periodicity is 2π.

  7. 25:00 – 30:00 25:00-30:00

    The sixth function, f(x) = sec x, is presented with the definition sec x = 1 / cos x, where cos x ≠ 0. The graph is drawn with vertical asymptotes at x = (2n+1)π/2. The graph consists of U-shaped curves above and below the x-axis, with peaks at y=1 and troughs at y=-1. The domain is R - {(2n+1)π/2}, the range is (-∞, -1] ∪ [1, ∞), and the periodicity is 2π.

  8. 30:00 – 33:44 30:00-33:44

    The video concludes with a 'Note' slide. The instructor writes the statement: 'All trig. functions are periodic :'. This summarizes the key property of the functions discussed, reinforcing that their graphs repeat at regular intervals.

The video systematically presents a complete analysis of the six primary trigonometric functions. It follows a consistent structure for each function: definition, graph construction, and determination of domain, range, and periodicity. The visual method of drawing the graphs on a coordinate plane, highlighting key points and asymptotes, provides a clear understanding of their behavior. The lecture effectively uses the unit circle concept (implied by the use of radians and standard values) to explain the functions. The final note serves as a powerful summary, emphasizing the fundamental periodic nature of all trigonometric functions, which is a core concept in trigonometry.

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