Graphs, Domain and Range of Trig Func

Duration: 34 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
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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