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Trigonometry Class 10 in One Shot 🔥 | Class 10 Maths Chapter 8 Complete Lecture | Shobhit Nirwan

Shobhit Nirwan・101 minutes read

Shob Ravan introduces Trigonometry in Class 10, emphasizing understanding concepts and practicing from various sources. The text delves into right-angle triangles, trigonometric ratios, and practical mnemonic devices for memorization.

Insights

  • Trigonometry concepts involve understanding right-angle triangles, hypotenuse, base, and perpendicular, with a focus on angle sum properties and the Pythagorean Theorem.
  • Trigonometric ratios like sin, cos, tan, cosec, sec, and cot are derived from the sides of a right-angle triangle, aiding in finding unknown sides and angles.
  • Practical tips for memorizing trigonometric ratios, emphasizing regular revision for better retention, and recalling during studies are crucial for mastering trigonometry concepts and problem-solving skills.

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Recent questions

  • What is the importance of practicing trigonometry questions?

    Practicing trigonometry questions is crucial for mastering concepts and formulas, leading to better problem-solving skills. Continuous practice enhances understanding and retention, ensuring success in trigonometry.

  • How can trigonometry equations be simplified effectively?

    Trigonometry equations can be simplified effectively by converting between trigonometric functions like cosine and sine. Proving the equality of Left Hand Side (LHS) and Right Hand Side (RHS) is essential, along with taking the Least Common Multiple (LCM) to simplify equations.

  • What are the recommended sources for studying trigonometry?

    To study trigonometry effectively, it is recommended to start with NCERT textbooks and then practice exercises and examples from resources like RD Sharma or RS Aggarwal. These sources provide comprehensive coverage of trigonometric concepts for better understanding.

  • How can one approach trigonometry problems systematically?

    To approach trigonometry problems systematically, it is advised to start with NCERT textbooks, practice exercises from reliable sources, and focus on mastering concepts and formulas. Systematic practice and understanding are key to solving trigonometry problems accurately.

  • Why is continuous practice essential in mastering trigonometry?

    Continuous practice is essential in mastering trigonometry as it enhances understanding, retention, and problem-solving skills. Shobhit Bhaiya emphasizes the importance of dedicated practice for success in trigonometry, offering support and guidance through lectures on the channel.

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Summary

00:00

Trigonometry Basics: Right Triangles, Ratios, Mnemonics

  • The text discusses taking five steps back from a pole with a step of 1 meter, positioning oneself 5 meters away from the pole at a 60-degree angle.
  • Shob Ravan introduces the topic of Trigonometry in Class 10, emphasizing understanding concepts and practicing questions from various sources like NCRT, RD, and RS.
  • The chapter delves into right-angle triangles, explaining the hypotenuse, base, and perpendicular, depending on the angle of observation.
  • The angle sum property of triangles is highlighted, stating that the sum of interior angles is always 180 degrees.
  • The Pythagorean Theorem is explained, where the square of the hypotenuse equals the sum of the squares of the other two sides, aiding in finding unknown sides.
  • Trigonometric ratios are introduced, focusing on ratios derived from the hypotenuse, base, and perpendicular of a right-angle triangle.
  • The concept of naming angles with Theta is discussed, with ratios like sin, cos, tan, cosec, sec, and cot derived from the sides of the triangle.
  • Practical tips for remembering trigonometric ratios are shared, like "Papa BD P" for sin, "Father will smoke bidi" for cos, and "Son, it is mine" for tan.
  • The importance of revising and recalling these ratios during studies is emphasized for better understanding and retention.
  • The text concludes by summarizing the key points covered, including right-angle triangles, trigonometric ratios, and practical mnemonic devices for memorization.

13:13

Trigonometry Basics and Pythagoras Theorem Explained

  • To remove the unknown side, apply Pythagoras theorem by squaring the perpendicular and base sides.
  • Trigonometry ratios involve taking ratios of perpendicular, base, and hypotenuse sides.
  • For finding the sine of an angle theta, divide the perpendicular by the hypotenuse.
  • To determine the angle theta, divide the base by the hypotenuse.
  • To find the hypotenuse angle theta, divide the perpendicular by the base.
  • For cosecant of angle theta, calculate the hypotenuse divided by the perpendicular.
  • To remember the trigonometry ratios, use the mnemonic "Papa BDP Ho G."
  • Utilize Pythagoras theorem to find the unknown side by squaring the known sides.
  • Calculate the square of the unknown side by subtracting the squares of the known sides.
  • Trigonometry ratios can be determined by dividing the sides of the triangle based on the given values.

26:01

Square Roots and Equations Explained

  • If s = p, then the square is equal to two.
  • The square root of 4k is 9.
  • The square root of 9k is 25.
  • The square root of 16 is 9k.
  • 3k is the square root of the perpendicular.
  • The value of alpha is p up b.
  • The value of 3b is 4k.
  • The LCM of 4 and 3 is 1/7.
  • The value of p is 24.
  • The values of o k and p k are 25 and 24 respectively.

40:31

Mastering Trigonometric Ratios and Functions

  • Trigonometric ratios: If two angles are equal, their trigonometric ratios are also equal.
  • Understanding the sign of an angle: Pronounce "sin" as "sine," not "sa*theta."
  • Multiplication inside trigonometric functions: Do not multiply inside, follow the correct procedure.
  • Squaring and cubing angles: The square of "a" is written as "sin^2 a," and the cube is written as "sin^3 a."
  • Negative powers: Inverse trigonometric functions are represented by negative powers.
  • Standard angles: Memorize the values of sin and cos for standard angles (0, 30, 45, 60, 90).
  • Inverse trigonometric functions: Understand the inverse values of trigonometric functions.
  • Cosecant and cotangent values: Know the values of cosec and cot for standard angles.
  • Practice and memorization: Regular practice and memorization are essential for recalling trigonometric values.
  • Application of trigonometric values: Apply the memorized values to solve trigonometric equations accurately.

52:05

Trigonometry Values and Right Triangle Dimensions

  • Value of tan60 is 1/√3
  • Value of cos60 is 1/2
  • Value of sec3 is 2/√3
  • Square of 2 is 1/4
  • Value of √3/2 is 3/4
  • tan3x = sin4
  • tan45 = 1
  • tan1 = 1/√2
  • Length of sides in a right triangle with angle 30 degrees and perpendicular of 5 cm: hypotenuse is 10 cm, base is √75 cm
  • Angle A in the triangle is 60 degrees

01:05:19

Trigonometry: Sine Ratio and Basic Identities

  • To find the hypotenuse and third side of a triangle, use the sine of the perpendicular and hypotenuse.
  • When determining an angle in a triangle, consider the given sides - if the perpendicular and hypotenuse are known, use the sine ratio to find the angle.
  • In a triangle with known sides, apply the sine ratio to calculate the angle.
  • To find the angle C in a triangle, use the sine ratio with the perpendicular and hypotenuse.
  • The height of a pole can be calculated using trigonometry by considering the angle and known sides of a triangle.
  • Trigonometric identities are based on three main formulas: sin^2θ + cos^2θ = 1, 1 + tan^2θ = sec^2θ, and 1 + cot^2θ = cosec^2θ.
  • Remember the three main trigonometric formulas: sinθ = perpendicular/hypotenuse, cosθ = base/hypotenuse, and tanθ = perpendicular/base.
  • Expressing trigonometric functions in terms of each other involves using the basic trigonometric identities and formulas.
  • When proving trigonometric equations, manipulate the left-hand side to match the right-hand side by applying trigonometric identities and formulas.
  • When solving trigonometric problems, focus on understanding and applying the basic trigonometric ratios and identities to find angles and side lengths accurately.

01:18:17

"Mathematical Equations: Simplify, Solve, Prove"

  • To bring trouble to someone, avoid cursing others.
  • Break down a coat with your signature.
  • Write a specific phrase to protect yourself.
  • Tighten your maximum time.
  • Solve a mathematical question involving a kiss.
  • Calculate and then find the least common multiple (LCM).
  • Simplify the equation by taking LCM.
  • Prove the equation by showing LHS equals RHS.
  • Convert tan3a to sa/k.
  • Use the formula to simplify the equation.

01:32:45

Solving Trigonometric Equations: Simplify and Solve

  • The text discusses solving mathematical equations using trigonometric functions.
  • It emphasizes the importance of simplifying equations by converting between trigonometric functions.
  • The process involves proving the equality of Left Hand Side (LHS) and Right Hand Side (RHS) of equations.
  • Instructions are given to switch focus from LHS to RHS when stuck in the process.
  • The text details steps to simplify equations by converting cosine to sine and vice versa.
  • It highlights the significance of taking the Least Common Multiple (LCM) to simplify equations.
  • The text provides a step-by-step guide on simplifying equations involving trigonometric functions.
  • It explains the process of taking square roots and simplifying expressions to reach the final solution.
  • Practical advice is given to approach trigonometry problems systematically by starting with NCERT textbooks.
  • The text recommends practicing exercises and examples from textbooks like RD Sharma or RS Aggarwal for a thorough understanding of trigonometry.

01:46:30

Master Trigonometry with Continuous Practice and Support

  • Trigonometry requires dedicated practice to master concepts and formulas, leading to better problem-solving skills. Shobhit Bhaiya emphasizes the importance of continuous practice for success, offering support and guidance through lectures on the channel.
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