Quant Ready Recokner-The ultimate formula booklet

 Line: Inclination of a Line: 

► The angle of inclination or simply an inclination of a line is the angle θ which the part of the line  above x-axis and measured in anticlockwise direction.    

 Remarks: 

► The inclination of x-axis is 0°.

► Let A be an acute angle of a right ΔABC in which ∠B = 90°.

1. sin A = perpendicular/hypotenuse ⇒ sin A = BC/AC

2. cosine A = base/hypotenuse ⇒ cos A = AB/AC

3. tangent A = perpendicular/base ⇒ tan A = BC/AB

4. cotangent A = base/perpendicular ⇒ cot A =AB/BC

5. secant A = hypotenuse/base ⇒ sec A = AC/AB

6. cosecant A = hypotenuse/ perpendicular ⇒ cosec A = AC/BC

Relations Between T-Ratios:

Polynomial

► f(x) = a₀ + a₁x + a₂x² + a₃x³+ ... +a_n–1x^n–1 + a_nxⁿ, where x is a variable, a > 0, (<0) are constants and a_n ≠ 0.

Example: 4x⁴ + 3x³ – 7x² + 5x + 3, 3x³ + x² – 3x + 5.

(1)    Real polynomial

f(x) = a₀ + a₁x + a₂x² + a₃x³ + ... +a_nxⁿ

is called real polynomial of real variable x with real coefficients.

Example:  3x³ – 4x² + 5x – 4, x² – 2x + 1 etc. are real polynomials.