Trigonometric Functions 01 | Introduction | Basics of Angle and Trigonometry | Class 11 | IIT JEE
Physics Wallah - Alakh Pandey・3 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.
