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Trigonometric Functions 01 | Introduction | Basics of Angle and Trigonometry | Class 11 | IIT JEE

Physics Wallah - Alakh Pandey・42 minutes read

Trigonometric Functions are introduced as a new business venture based on foundational concepts from tenth-grade Trigonometry. The text emphasizes the importance of understanding angles, measurements, conversions, and trigonometric identities for practical applications and competitive exams.

Insights

  • Trigonometric Functions are built upon the foundation of understanding angles, rotations, and conversions between degrees and radians, with a focus on the significance of Indian mathematicians' contributions to their development.
  • The text emphasizes the importance of mastering trigonometric identities, including detailed proofs, conversions between measurement systems, and practical applications in right-angled triangles, urging readers to engage in self-proofing and collaborative learning to deepen their understanding of trigonometry.

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  • What is the foundation for understanding Trigonometric Functions?

    The chapter on Trigonometry in the tenth grade.

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Summary

00:00

Introduction to Trigonometric Functions in Business

  • Trigonometric Functions are being introduced as a new business venture.
  • The chapter on Trigonometry in the tenth grade is the foundation for understanding Trigonometric Functions.
  • Trigonometric Functions involve dealing with signs as functions to the standard second president.
  • Plane trigonometry, also known as plane trigonometry, focuses on angles made in the back plane.
  • Indian mathematicians have made significant contributions to the development of trigonometric functions.
  • The angle is defined by the ratio of the arc length to the radius of a circle.
  • An angle is positive if formed in an anti-clockwise direction and negative if formed clockwise.
  • The SI unit of an angle is the radian, calculated by dividing the arc length by the radius.
  • The angle can be zero, positive, or negative, with measurements in degrees or radians.
  • Angles can exceed 360 degrees, with rotations beyond a full revolution resulting in larger angles.

16:01

Converting Angles: Degrees to Radians Explained

  • The angle can be infinite and very large, with the possibility of approaching infinity.
  • Rotating an object continuously in one direction can lead to a very large angle forming.
  • Rotating in a clockwise direction can result in the angle increasing and potentially reaching infinity.
  • There are two main systems of measuring angles: degree measurement and radian measurement.
  • Degree measurement is popular among students, while radian measurement involves placing a small 'c' above a number.
  • The relationship between degree and radian measurements is crucial for converting angles between the two systems.
  • One degree is equal to 60 minutes, and one minute is further divided into 60 seconds for precise angle measurement.
  • The conversion between degrees and radians involves multiplying or dividing by specific values.
  • Understanding the relationship between degrees, minutes, and seconds is essential for accurate angle measurement.
  • Converting angles from degrees to radians involves specific calculations based on the relationship between the two measurement systems.

31:31

"Revolution Media: Numbers, Angles, Trigonometry Explained"

  • Revolution Media has a Number of Relations Manager who explains the significance of numbers for Revolution.
  • The concept of a revolution is illustrated through hair, scar lines, and angles.
  • One revolution is equivalent to 360 degrees in degree measurement.
  • The text delves into the basics of angles and presents a question involving circles and angles.
  • The question involves finding the ratio of radii in circles with specific angles.
  • The process of converting degrees into radians is explained, with detailed calculations provided.
  • Trigonometric ratios and their applications in right-angled triangles are discussed.
  • The six trigonometric ratios are explained based on the sides of a triangle, with six possibilities arising.
  • Trigonometric identities, including Pythagoras Theorem, are detailed, emphasizing their importance in trigonometry.
  • The proof of trigonometric identities is highlighted, stressing the significance of understanding the roots of trigonometric concepts for better comprehension.

47:27

Mastering Trigonometric Identities for Competitive Exams

  • The proof of theta minus cos squared theta is emphasized, with the suggestion to follow the provided advice to achieve proof independently.
  • Various trigonometric identities are introduced, with a focus on the importance of remembering and understanding them for competitive exams.
  • A specific mathematical equation is detailed, showcasing the process of simplification and substitution to reach a known trigonometric identity.
  • The text encourages self-proofing of mathematical identities, with a call to action for readers to share their proofs in the comments section for further discussion and learning.
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