Basic Mathematics for Physics
N E E T PRE PA R ATI O N CH A PTE R N OTES & FO R M U L A S H E E T
1. Trigonometry
Angle Measurement & Basics
• Radian to Degree Conversion: π rad = 180° &implies; 1 rad ≈ 57.3°
• Formula: θ (in rad) = s / r (where s = arc length, r = radius)
Fundamental Ratios & Identities
• sin θ = P / H, cos θ = B / H, tan θ = P / B
• sin2θ + cos2θ = 1 | 1 + tan2θ = sec2θ | 1 + cot2θ = csc2θ
Standard Values Table
θ 0° 30° 37° 45° 53° 60° 90°
sin θ 0 1/2 3/5 1/√2 4/5 √3/2 1
cos θ 1 √3/2 4/5 1/√2 3/5 1/2 0
tan θ 0 1/√3 3/4 1 4/3 √3 &infty;
Quadrant Rules (ASTC Rule)
• Q1 (0° - 90°): All ratios are positive.
• Q2 (90° - 180°): Sine & Cosecant are positive.
• Q3 (180° - 270°): Tangent & Cotangent are positive.
• Q4 (270° - 360°): Cosine & Secant are positive.
Double-Angle & Compound Angle Formulas
• sin(A ± B) = sin A cos B ± cos A sin B
• cos(A ± B) = cos A cos B ∓ sin A sin B
• sin(2θ) = 2 sinθ cosθ
• cos(2θ) = cos2θ - sin2θ = 2cos2θ - 1 = 1 - 2sin2θ
Small Angle Approximations (for θ ≪ 1 rad)
sin θ ≈ θ | tan θ ≈ θ | cos θ ≈ 1
2. Differential Calculus
Used to find instantaneous rates of change (e.g., Velocity v = dx/dt, Acceleration a = dv/dt).
Standard Derivatives
• d/dx (xn) = n xn-1 • d/dx (c) = 0 (constant)
NEET Physics Express Notes — Basic Mathematics Page 1 of 3
N E E T PRE PA R ATI O N CH A PTE R N OTES & FO R M U L A S H E E T
1. Trigonometry
Angle Measurement & Basics
• Radian to Degree Conversion: π rad = 180° &implies; 1 rad ≈ 57.3°
• Formula: θ (in rad) = s / r (where s = arc length, r = radius)
Fundamental Ratios & Identities
• sin θ = P / H, cos θ = B / H, tan θ = P / B
• sin2θ + cos2θ = 1 | 1 + tan2θ = sec2θ | 1 + cot2θ = csc2θ
Standard Values Table
θ 0° 30° 37° 45° 53° 60° 90°
sin θ 0 1/2 3/5 1/√2 4/5 √3/2 1
cos θ 1 √3/2 4/5 1/√2 3/5 1/2 0
tan θ 0 1/√3 3/4 1 4/3 √3 &infty;
Quadrant Rules (ASTC Rule)
• Q1 (0° - 90°): All ratios are positive.
• Q2 (90° - 180°): Sine & Cosecant are positive.
• Q3 (180° - 270°): Tangent & Cotangent are positive.
• Q4 (270° - 360°): Cosine & Secant are positive.
Double-Angle & Compound Angle Formulas
• sin(A ± B) = sin A cos B ± cos A sin B
• cos(A ± B) = cos A cos B ∓ sin A sin B
• sin(2θ) = 2 sinθ cosθ
• cos(2θ) = cos2θ - sin2θ = 2cos2θ - 1 = 1 - 2sin2θ
Small Angle Approximations (for θ ≪ 1 rad)
sin θ ≈ θ | tan θ ≈ θ | cos θ ≈ 1
2. Differential Calculus
Used to find instantaneous rates of change (e.g., Velocity v = dx/dt, Acceleration a = dv/dt).
Standard Derivatives
• d/dx (xn) = n xn-1 • d/dx (c) = 0 (constant)
NEET Physics Express Notes — Basic Mathematics Page 1 of 3
