Trigonometry : Course in Mathematics for the IIT-JEE and Other Engineering Entrance Examinations

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Cover Contents Preface Part A: Trigonometric Functions and Identities Lecture 1: Measurement of Angles Basic Concepts 1. Measurement of an Angle 2. Sense of an Angle 2.1 Types of Angles 2.2 Coterminal Angles 3. Systems of Measuring Angles 3.1 Sexagesimal System 3.2 Centesimal System 3.3 Circular System 4. Relation between θ, L and R 5. Relation between Three Systems of Measurement of an Angle 5.1 Conversion Formula 6. Relation between Degree and Radian 6.1 Value of π = 227Or 355113Or 3.141592 Soled Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 2: Trigonometric Functions Basic Concepts 1. Table Representing All Trigonal Ratios (TRs) in Terms of One Trigonal Ratio 2. T-Ratios (or Trigonometric Functions) 3. Following are Some of the Fundamental Trigonometric Identities 4. Maximum and Minimum Values of Trigonometrical Functions 5. Some Useful Results Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 3: Quadrants Basic Concepts 1. Quadrants 2. Change in Function Connected with Related Angles 3. Value of TR in Terms of an Angle in the First Quadrant 4. Important TR Value's 5. Trigonometry Ratios of Standard Angles Solved Objective Problems: Helping Hand Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 4: Trigonometric Functions of Compound Angles Basic Concepts 1. Trigonometric Functions for Sum and Difference of the Two Angles 2. Trigonometric Ratios of Some Useful Angles 3. Maximum and Minimum Values of Some Functions 4. Some Important Functions Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 5: Sum and Difference of Two Angles Basic Concepts 1. Formulae Converting Product Into Sum or Difference 2. Formulae Converting Sum and Difference Into Product 3. Trigonometric Functions for Sum of Three of More Angles Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 6: Trigonometric Ratios of Multiple and Sub-Multiple Angles Basic Concepts 1. Formulae of Double, Triple and Half Angles 2. Some Useful Results 3. Results Involving Sin 2A and Cos 2A Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 7: Identities of Trigonometric Functions Basic Concepts 1. if a + B + C = 180°, Then 2. if a + B + C = 2 Π, Then Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 8: Graphs of Trigonometric Functions Basic Concepts 1. Periodicity of Trigonometric Functions 2. Graphs of Trigonometrical Functions 2.1 Graph of Sin X, for 0 ≤ X ≤ 2π 2.2 Graph of Cos X, for 0 ≤ X ≤ 2π 2.3 Graph of Tan X, for 0 ≤ X ≤ 2π 2.4 Graph of Cot X, for 0 ≤ X ≤ 2π 2.5 Graph of Sec X, for 0 ≤ X ≤ 2π 2.6 Graph of Cosec X, for 0 ≤ X ≤ 2π 3. Domain and Range of Trigonometric Functions Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Part B: Trigonometric Equations and Inequalities Lecture 1: Trigonometric Equations Basic Concepts 1. Trigonometric Equation 2. Kinds of Trigonometric Equation 3. Solution of a Trigonometric Equation 4. General Solutions and Principal Solutions 5. General Solutions of Trigonometric Equations 5.1 Based on Sin θ and Cosec θ in their Domains 5.2 Based on Cos θ and Sec θ in their Domain 5.3 Based on Tan θ and Cot θ in their Domain 5.4 Based on Two Equations in One Variable 5.5 Solution of the Equations of the Form Ofa Cos θ ± B Sin θ = C 6. Some Useful Hints for Solving Trigonometric Equations Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Part C: Properties and Solutions of Triangles Lecture 1: Properties of Triangles-I Basic Concepts 1. Properties of Triangles 2. Law of Sines or Sine Rule 3. Law of Tangents or Tangent Rule (Napiers Analogy) 4. Law of Cosines or Cosine Formula 5. Projection Formula 6. Half Angle Formulae or Semi-Sum Formulae (I) Area of a Triangle 7. (I) Area of a Triangle (II) Hero’s Formula Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 2: Properties of Triangles-II Basic Concepts 1. Circumcircle of a Triangle 2. Incircle of a Triangle 3. Escribed Circles of a Triangle 4. Orthocentre of a Triangle 4.1 The Distances of the Orthocentre from the Vertices 4.2 Area, Side and Angle of Pedal 5. Cyclic Quadrilateral 6. Regular Polygon 6.1 Radius of Circumcribing Circle 6.2 Radius of Inscribed Circle 6.3 Area of the Polygon 7. Orthocentre 8. Circum-Centre, Centroid Andorthocentre are Collinear 9. Bisectors of the Angles 10. Radii of the Inscribed and Circumscribing Circles of a Regular Polygon 11. Area of a Regular Polygon Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Part D: Inverse Trigonometric Functions Lecture 1: Inverse Trigonometric Function Basic Concepts 1. Inverse Functions 2. Domain and Range of Inverse Trigonometric Functions 3. Some Important Formulae Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Part E: Heights and Distances Lecture 1: Heights and Distances Basic Concepts Formula Solved Subjective Problems (XII Board (C.B.S.E./State)): For Better Understanding and Concept Building of the Topic Unsolved Subective Problems (XII Board (C.B.S.E./State)): Solve these Problems to Grasp the Topic Answers Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Hints and Explanations Unsolved Objective Problems (Identical Problems for Practice): For Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Part F: Test Your Skills Lecture 1: Test Your Skills Assertion/Reasoning 1 Assertion and Reasoning Type Questions Assertion/Reasoning: Solutions 1 Assertion/Reasoning 2 Assertion and Reasoning Type Questions Assertion/Reasoning 2 Assertion/Reasoning 3 Assertion and Reasoning Type Questions Assertion/Reasoning 3 Topicwise Warmup Test Topicwise Warmup Test: Solution Question Bank Answers