Values at Allied Angles

Duration: 17 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 is a comprehensive lecture on trigonometric functions at allied angles, designed for students preparing for competitive exams. The instructor begins by introducing the concept of allied angles, which are angles related to a base angle θ by addition or subtraction of multiples of π/2, π, or 2π. The core of the lesson is a systematic method for simplifying trigonometric expressions involving these angles, using a unit circle diagram. The method involves two key rules: (1) if the angle is measured from the x-axis (e.g., π+θ, 2π-θ), the trigonometric function changes (sin to cos, tan to cot, etc.); (2) if the angle is measured from the y-axis (e.g., π/2+θ, 3π/2-θ), the function does not change. The sign of the result is determined by the quadrant in which the angle lies. The video demonstrates this method with several examples, including sin(π/2+θ) = cosθ and sin(π+θ) = -sinθ. It also covers the periodicity and domain of the cotangent function and provides a worked example to calculate the value of a complex expression involving cot²(π/6), csc(5π/6), and tan²(π/6), arriving at the final answer of 6.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide, "Trigonometric Functions at Allied Angles," and presents a list of expressions to be simplified, such as sin(π/2+θ) and sin(π+θ). The instructor begins to explain the concept of allied angles, which are angles related to a base angle θ by addition or subtraction of π/2, π, or 2π. He starts to draw a unit circle, labeling the x and y axes, and begins to mark the standard angles: π/2, π, 3π/2, and 2π, setting the stage for the graphical method.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to build the unit circle diagram, labeling the four quadrants and the angles in each. He introduces the concept of a base angle θ, which is assumed to be in the first quadrant (acute). He then draws the angles π/2+θ, π-θ, π+θ, and 3π/2-θ, showing their positions on the circle. He explains that the sign of the trigonometric function depends on the quadrant. He introduces the first rule: when the angle is measured from the x-axis (e.g., π+θ), the function changes (sin to cos, tan to cot, etc.). He writes this rule as "X-axis → fun. change".

  3. 5:00 – 10:00 05:00-10:00

    The instructor completes the unit circle diagram, labeling all the allied angles. He introduces the second rule: when the angle is measured from the y-axis (e.g., π/2+θ), the function does not change. He writes this as "Y-axis → fun. change". He then provides a list of function changes: sin → cos, tan → cot, sec → cosec. He demonstrates the application of these rules with examples, such as sin(π/2+θ) = cosθ and sin(π+θ) = -sinθ, explaining the sign based on the quadrant. He also shows that the period of the cotangent function is π.

  4. 10:00 – 15:00 10:00-15:00

    The instructor transitions to a new section, writing down the formulas for trigonometric functions of negative angles and angles greater than 2π. He shows that sin(2π-θ) = sin(-θ) = -sinθ, cos(2π-θ) = cos(-θ) = cosθ, and so on. He summarizes the key identities for negative angles: sin(-θ) = -sinθ, cos(-θ) = cosθ, tan(-θ) = -tanθ, cot(-θ) = -cotθ, sec(-θ) = secθ, and cosec(-θ) = -cosecθ. He emphasizes that sine, tangent, cotangent, and cosecant are odd functions, while cosine and secant are even functions.

  5. 15:00 – 16:33 15:00-16:33

    The video concludes with a worked example. The question asks for the value of cot²(π/6) + cosec(5π/6) + 3tan²(π/6). The instructor substitutes the known values: cot(π/6) = √3, so cot²(π/6) = 3; tan(π/6) = 1/√3, so 3tan²(π/6) = 3*(1/3) = 1; and cosec(5π/6) = 1/sin(5π/6) = 1/sin(π-π/6) = 1/sin(π/6) = 1/(1/2) = 2. The final calculation is 3 + 2 + 1 = 6. The answer is (b) 6.

The video provides a structured and visual approach to mastering trigonometric identities for allied angles. It begins with a clear definition and a graphical representation using the unit circle, which is the foundation for the entire lesson. The core of the teaching is a two-part rule system based on the axis of measurement (x-axis or y-axis), which simplifies the process of determining both the function and its sign. This method is systematically applied to various examples, reinforcing the concept. The lesson is well-organized, moving from foundational concepts to a practical application in a final problem, making it an effective revision tool for students.

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