NCERT Class 11 Maths Chapter 3 Trigonometric Function: Notes, Mind Map and Assertion Questions

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Welcome to our comprehensive guide to CBSE Class 11 Maths Chapter 3: Trigonometric Function. In this article, we provide you with detailed notes, a mind map, and assertion questions to help you understand and master this important topic. Trigonometric functions are fundamental not only in mathematics but also in various fields such as physics, engineering, and computer science.

They form the basis of understanding the relationships between angles and sides of triangles, making them crucial in solving real-world problems. Our notes cover all the concepts and formulas related to trigonometric functions, making them an invaluable resource for students studying for their Class 11 examinations. To aid in visualizing the connections between different concepts, we have also included a mind map.

This visual representation will help you grasp the interrelationships between various trigonometric functions and their properties. Finally, our article features assertion questions to test and reinforce your understanding of the topic. These questions are designed to challenge you and deepen your knowledge. Whether you are a student preparing for exams or someone seeking a solid understanding of trigonometry, our comprehensive guide has you covered. Let's dive in and unlock the mysteries of trigonometric functions together.

Class 11 Maths, Chapter 3 is all about trigonometric functions. These are a special set of functions that are really important in maths. Trigonometric functions help us understand things like angles and triangles, which are used a lot in different areas, like engineering and physics.

To get good at these, you can practice with Assertion Reason questions. These are questions where you have to figure out if statements are true and why they are true. It's like being a math detective!

In class, you'll learn about different kinds of trigonometric functions and how to use them. Your teacher might give you notes which are super helpful because they explain everything step by step. Sometimes, you might also see a mind map in class. Mind maps are like big diagrams that show how all the ideas in trigonometry are connected. They're really useful to see the big picture.

You'll also get to do lots of practice questions. Some of these will be multiple choice questions (MCQs), where you pick the right answer from a few choices. These are good for testing your knowledge quickly.

There are also extra questions and important questions in trigonometry. These might be a bit harder, but they're great for making sure you really understand everything. And if you get stuck, there's always a worksheet with solutions that can help you figure out the answers.

So, remember, trigonometric functions are a key part of Class 11 Maths, and practicing with different types of questions will really help you get better at it!

class 11 trigonometric formulas:

  1. Basic Trigonometric Ratios:

    • Sine (sin): For a right-angled triangle, sin of an angle is the length of the opposite side divided by the length of the hypotenuse.
    • Cosine (cos): It's the length of the adjacent side divided by the hypotenuse.
    • Tangent (tan): It's the length of the opposite side divided by the length of the adjacent side.
  2. Reciprocal Relations:

    • Cosecant (cosec) = 1/sin
    • Secant (sec) = 1/cos
    • Cotangent (cot) = 1/tan
  3. Pythagorean Identities:

    • sin²θ + cos²θ = 1
    • 1 + tan²θ = sec²θ
    • 1 + cot²θ = cosec²θ
  4. Trigonometric Ratios of Specific Angles:

    • sin, cos, and tan values for 0°, 30°, 45°, 60°, and 90°.
  5. Trigonometric Ratios of Complementary Angles:

    • sin(90° - θ) = cosθ
    • cos(90° - θ) = sinθ
    • tan(90° - θ) = cotθ
    • cot(90° - θ) = tanθ
    • sec(90° - θ) = cosecθ
    • cosec(90° - θ) = secθ
  6. Compound Angle Formulas:

    • sin(A + B) = sinA cosB + cosA sinB
    • cos(A + B) = cosA cosB - sinA sinB
    • tan(A + B) = (tanA + tanB) / (1 - tanA tanB)
  7. Half-Angle Formulas:

    • sin²(θ/2) = (1 - cosθ) / 2
    • cos²(θ/2) = (1 + cosθ) / 2

functions of trigonometry:

  1. Sine (sin): This function relates the angle in a triangle to the ratio of the length of the side opposite the angle to the length of the longest side of the triangle (the hypotenuse). It's written as sin(θ), where θ is the angle.

  2. Cosine (cos): Cosine is similar to sine, but it relates the angle to the ratio of the length of the side adjacent to the angle and the hypotenuse. It's written as cos(θ).

  3. Tangent (tan): This function compares the length of the side opposite the angle to the length of the side adjacent to it. It's written as tan(θ).

  4. Cosecant (cosec): It's the reciprocal of sine. So, cosec(θ) = 1/sin(θ).

  5. Secant (sec): This is the reciprocal of cosine. So, sec(θ) = 1/cos(θ).

  6. Cotangent (cot): It's the reciprocal of tangent. So, cot(θ) = 1/tan(θ).

    Basic Trigonometric Ratios:

    In trigonometry, the basic ratios are sine (sin), cosine (cos), and tangent (tan). These ratios are used to relate the angles of a triangle to the lengths of its sides. For a right-angled triangle, sin is the ratio of the opposite side to the hypotenuse, cos is the adjacent side to the hypotenuse, and tan is the opposite side to the adjacent side.

    Trigonometric Identities:

    Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables. The most common ones are the Pythagorean identities, like sin²θ + cos²θ = 1, and angle sum and difference identities, like sin(A + B) = sinA cosB + cosA sinB.

    Trigonometric Functions of Special Angles:

    This refers to the values of the trigonometric functions at specific angles such as 0°, 30°, 45°, 60°, and 90°. For example, sin 45° = 1/√2, cos 30° = √3/2.

    Graphs of Trigonometric Functions:

    The graphs of trigonometric functions show how the values of sin, cos, and tan change over a cycle. These graphs are wave-like patterns that repeat every 360° or 2π radians.

    Inverse Trigonometric Functions:

    Inverse trigonometric functions are the inverses of the basic trigonometric functions. They are used to find an angle when the value of the trigonometric function is known. The main ones are arcsin, arccos, and arctan.

    Trigonometric Equations and Inequalities:

    These are equations and inequalities that involve trigonometric functions. Solving them often involves using trigonometric identities and algebraic methods.

    Applications of Trigonometry:

    Trigonometry is used in various fields like physics, engineering, astronomy, and even in everyday life for solving problems involving angles and distances.

    Mind Map for Trigonometric Functions:

    A mind map for trigonometric functions would include all the main concepts like the basic ratios, identities, graphs, and applications, linked together in a visual diagram. This helps in understanding how all the concepts are related and in remembering them better.

    Assertion Questions for Trigonometric Functions:

    Assertion questions are a type of question where you are given two statements, and you have to determine if each statement is true and if the second statement is a correct explanation of the first. These are great for testing your understanding of trigonometric functions and concepts.

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