Quadratic Formula and Trigonometric Functions

Quadratic Formula

• The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a, where ax² + bx + c = 0.

Trigonometric Functions

• sin A = a / c, sin B = b / c, sin C = c / c
• c² = a² + b² - 2ab cos C
• cos α + cos β = 2 cos ((a + b) / 2) cos ((a - b) / 2)
• cos α - cos β = -2 sin ((a + b) / 2) sin ((a - b) / 2)

Mathematical Signs and Symbols

• = (equals)
• ≅ (equals approximately)
• ~ (is the order of magnitude of)
• > (greater than)
• >> (much greater than)
• 0 (upward and downward motion)

Binomial Theorem

• (1 - x)ⁿ = 1 - nx + nx(n-1)x² / 2! - nx(n-1)(n-2)x³ / 3! + ...
• (1 - x)⁻ⁿ = 1 + nx + nx(n+1)x² / 2! + nx(n+1)(n+2)x³ / 3! + ...

Physics Textbook

• The physics textbook is divided into two parts, with 15 chapters in total.
• The textbook development team aims to help students appreciate the beauty and logic of physics.

National Curriculum Framework

• The National Curriculum Framework-2005 (NCF-2005) was revised during a curriculum renewal process at the school level.
• The higher secondary stage syllabus was developed accordingly.

Physics in Other Branches

• Physics is basic to the understanding of almost all branches of science and technology.
• Physics concepts are increasingly being used in other branches such as economics and commerce, and behavioral sciences.

Quarks and Gluons

• The three quarks within a proton can sometimes appear to be free, although no free quarks have ever been observed.
• Quarks have a quantum mechanical property called 'color' and interact with each other through the exchange of particles called 'gluons'.

CARTOSAT-1

• CARTOSAT-1 is a state-of-the-art remote sensing satellite built by ISRO.
• It has a mass of 156 kg at lift-off and was launched into a 618 km high polar Sun Synchronous Orbit (SSO) by ISRO's Polar Satellite Launch Vehicle, PSLV-C6.
• It is mainly intended for cartographic applications.

Units and Measurement

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit.
• The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit.
• There are seven base units in the SI system, which are used for international usage in scientific, technical, industrial, and commercial work.

SI Units

• The SI units used the decimal system, making conversions within the system simple and convenient.
• The unit for plane angle is radian (rad) and the unit for solid angle is steradian (sr).

Quiz covering the quadratic formula and trigonometric functions of angles, including triangular relationships and calculations.