Functions Value at Quadrantal and Multiple Angles

Duration: 19 min

This video lesson is available to enrolled students.

Return to /learn/BPSC/part-2-primary-maths/trigonometry/trigonometric-functions-and-angles/asset-functions-value-at-quadrantal-and-multiple-angles after enrolling

Inside: a video lesson and guided study material.

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 trigonometric functions, beginning with an introduction to the six primary functions: sine, cosine, tangent, cotangent, secant, and cosecant. The instructor first presents the fundamental trigonometric identities, such as sin²θ + cos²θ = 1, and then displays a detailed table of values for these functions at key angles (0°, 30°, 45°, 60°, 90°). The core of the lesson focuses on the unit circle, where the coordinates of a point on the circle are defined as (cosθ, sinθ), allowing for the extension of trigonometric functions to all real numbers. The video explains how to find the values of trigonometric functions for any angle using the unit circle and demonstrates the periodic nature of these functions by showing how their values repeat at intervals of 2π. The instructor derives the general solutions for when sinθ = 0 and cosθ = 0, presenting the formulas θ = nπ and θ = (2n+1)π/2 respectively, where n is an integer. The lecture concludes with a discussion on the domain and range of the trigonometric functions, emphasizing that the domain is all real numbers for sine and cosine, while the range is [-1, 1].

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide reading "Trigonometric functions:". The instructor then lists the six primary trigonometric functions: sinθ, cosθ, tanθ, cotθ, secθ, and cscθ. He explains that these functions are defined as ratios of the sides of a right-angled triangle, with sinθ = P/H, cosθ = B/H, and tanθ = P/B, where P is the perpendicular, B is the base, and H is the hypotenuse. The instructor also introduces the concept of a function, f(θ), and begins to list the six trigonometric functions as f(θ) = sinθ, f(θ) = cosθ, etc.

  2. 2:00 – 5:00 02:00-05:00

    The instructor transitions to the concept of the unit circle, explaining that it is a circle with a radius of 1 unit. He draws a coordinate system and a circle centered at the origin. He explains that for any angle θ, the coordinates of the point where the terminal side of the angle intersects the unit circle are (cosθ, sinθ). This is a key concept, as it allows the definition of trigonometric functions for any real number, not just acute angles. The instructor then shows a table of values for trigonometric functions at standard angles (0°, 30°, 45°, 60°, 90°), which is a common reference for students.

  3. 5:00 – 10:00 05:00-10:00

    The instructor explains the periodic nature of trigonometric functions, showing that their values repeat every 2π radians. He draws a diagram of the unit circle and labels the angles in radians (0, π/2, π, 3π/2, 2π). He then derives the general solution for when sinθ = 0, stating that this occurs at angles that are integer multiples of π, which is written as θ = nπ, where n is an integer. He also derives the general solution for when cosθ = 0, which occurs at odd multiples of π/2, written as θ = (2n+1)π/2, where n is an integer. This is a crucial step in understanding the complete set of solutions for trigonometric equations.

  4. 10:00 – 15:00 10:00-15:00

    The instructor continues to build on the unit circle concept, showing how the values of sine and cosine are determined by the coordinates of a point on the circle. He explains that for a point (x, y) on the unit circle, x = cosθ and y = sinθ. He then discusses the domain and range of the trigonometric functions. The domain of sinθ and cosθ is all real numbers, while the range is [-1, 1]. For the other functions, the domain is restricted where the denominator is zero (e.g., tanθ is undefined when cosθ = 0). The instructor emphasizes that the unit circle is the foundation for understanding trigonometric functions beyond the right-angled triangle.

  5. 15:00 – 19:13 15:00-19:13

    The video concludes with a summary of the key points. The instructor reiterates the definitions of the six trigonometric functions and their relationship to the unit circle. He emphasizes that the unit circle allows for the extension of trigonometric functions to all real numbers. He also reviews the general solutions for sinθ = 0 and cosθ = 0, which are θ = nπ and θ = (2n+1)π/2, respectively. The final message is that understanding the unit circle is essential for mastering trigonometry, as it provides a geometric interpretation of the functions and their periodic behavior.

The video presents a structured and logical progression of concepts in trigonometry. It begins with the foundational definitions of trigonometric ratios from a right-angled triangle, then seamlessly transitions to the more powerful and general concept of the unit circle. This transition is the central theme, as the unit circle is used to define the functions for all real numbers and to explain their periodic nature. The instructor effectively uses diagrams, equations, and a table of values to illustrate these concepts. The lesson culminates in the derivation of general solutions for trigonometric equations, demonstrating the practical application of the unit circle. The overall synthesis is that trigonometric functions are not limited to acute angles but are periodic functions defined on the entire real number line, with the unit circle serving as the fundamental geometric model.

Loading lesson…