Sign of Trig Functions

Duration: 9 min

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Module outline

  1. Quantitative Aptitude: Number System, Divisibility Rules, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Partnership, Age Problems, Time and Work, Pipe and Cistern, Speed Time and Distance, Algebra, Arithmetic, Data Interpretation, Sequence and Series (Series), Logarithm, Powers and Exponents (Surds and Indices), Permutation and Combination, Probability, Speed Mathematics and Basic Mathematics, Trigonometry
  2. Logical Reasoning: Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Syllogisms, Inequality, Data Sufficiency, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Venn Diagram, Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Noun, Pronoun, Adjectives, Verb, Adverb, Tenses, Subject Verb Agreement (Verb Noun Agreement), Articles, Preposition, Conjunction, Modals, Determiner, Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  4. Data Structures (Domain Test): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Algorithms (Domain Test): Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms
  6. OOPs (Domain Test): Object Oriented Programming (OOPS)
  7. DBMS (Domain Test): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  8. SQL (Domain Test): SQL
  9. Operating Systems (Domain Test): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Domain Test): 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, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  12. Written English Test: English Writing Ability
  13. Psychometric Test: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lesson on the signs of trigonometric functions in the four quadrants of the coordinate plane. The instructor begins by setting up a standard Cartesian coordinate system, labeling the x and y axes, and then proceeds to define the quadrants. Key angles, including 0, π/2, π, 3π/2, and 2π, are marked on the axes to establish the boundaries of the quadrants. The core of the lesson is the explanation of the ASTC rule (All Students Take Calculus), which is a mnemonic to remember the signs of the trigonometric functions in each quadrant: All (sine, cosine, tangent) are positive in the first quadrant; Sine is positive in the second; Tangent is positive in the third; and Cosine is positive in the fourth. The video also includes a brief demonstration of the unit circle to explain the definitions of sine and cosine as the y and x coordinates of a point on the circle, respectively. Finally, the video presents a table of standard trigonometric values for angles 0°, 30°, 45°, 60°, and 90°, showing the values for sine, cosine, tangent, cotangent, secant, and cosecant, including cases where the function is undefined (N.D.).

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with the title 'Sign of Trigonometric functions' written in blue on a black background. The instructor draws a standard Cartesian coordinate system, labeling the horizontal axis as 'x' and the vertical axis as 'y'. He then marks the origin as 'O' and proceeds to label the key angles on the axes: π/2 at the top of the y-axis, π on the negative x-axis, 3π/2 at the bottom of the y-axis, and 2π on the positive x-axis. The instructor explains that these angles divide the plane into four quadrants, which are numbered I, II, III, and IV in an anti-clockwise direction, starting from the positive x-axis.

  2. 2:00 – 5:00 02:00-05:00

    The instructor labels the four quadrants as 'Ist Qua.', 'IInd Qua.', 'IIIrd Qua.', and 'IVth Qua.' in their respective positions. He then introduces the concept of 'Quadrantal Angles' and lists them as 0, π/2, π, 3π/2, and 2π. The main focus shifts to the signs of the trigonometric functions. The instructor writes the mnemonic 'ASTC' in a red box. He explains that in the first quadrant, all trigonometric functions (sin, cos, tan, cot, sec, cosec) are positive. In the second quadrant, only sine (sin) is positive. In the third quadrant, only tangent (tan) is positive. In the fourth quadrant, only cosine (cos) is positive. He uses the mnemonic 'All Students Take Calculus' to help remember this, with the first letter of each word corresponding to the functions that are positive in each quadrant.

  3. 5:00 – 8:49 05:00-08:49

    The instructor continues to elaborate on the signs of the trigonometric functions in each quadrant, writing 'sin +ve', 'cos +ve', 'tan +ve', 'cot +ve', 'sec +ve', and 'cosec +ve' in the first quadrant, and then 'sin +ve', 'cos -ve', 'tan -ve', 'cot -ve', 'sec -ve', 'cosec +ve' in the second quadrant, and so on for the other quadrants. He then draws a unit circle to explain the definitions of sine and cosine. He shows a point P on the circle with coordinates (cosθ, sinθ) and explains that sinθ = y/r and cosθ = x/r, where r is the radius. The video then transitions to a table titled 'Values at angles' which lists the values of sinθ, cosθ, tanθ, cotθ, secθ, and cosecθ for angles 0°, 30°, 45°, 60°, and 90°. The table shows that for 90°, tanθ and secθ are undefined (N.D.), and for 0°, cotθ and cosecθ are undefined (N.D.).

The video systematically teaches the sign conventions of trigonometric functions across the four quadrants of the coordinate plane. It begins with the foundational setup of the coordinate system and the definition of quadrants. The core of the lesson is the ASTC mnemonic, which provides a clear and memorable rule for determining the sign of any trigonometric function based on the quadrant in which the angle lies. The lesson is reinforced with a visual aid of the unit circle, which grounds the abstract concept in a geometric definition. The video concludes with a practical table of standard trigonometric values, which is essential for solving problems and understanding the behavior of these functions at key angles.

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