Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Cartesian Coordinate System & Polar Coordinate System

Cartesian Co-ordinate System: 

The plane of  x   and  y – axis is known as the coordinate plane or the Cartesian Plane.

The Four Quadrants:

First Quadrant  Q_1 = interior of <  xoy

Second Quadrant  Q_2 = interior of <  x'oy

Third Quadrant  Q_3 = interior of <  x'oy'

Fourth Quadrant  Q_4 = interior of <  xoy'

By the definition of Cartesian Coordinates:

(i)  P(x, y) \in Q_1 \Leftrightarrow x >0, \quad y >0

(ii)  P (x,y) \in Q_2\Leftrightarrow x < 0 , \quad y > 0  

(iii)  P (x,y)\in Q_3\Leftrightarrow x<  0, \quad y < 0

(iv)  P (x,y) \in Q_4\Leftrightarrow x >  0 , \quad y <  0

Polar Coordinate System:

The position of a point in the Cartesian plane with respect to the positive  x  -axis  \overrightarrow{OX} and the origin  O . In this system   \overrightarrow{OX} and  O are known as the intitial ray and the pole respectively.

Definition of  (r,\theta) for  r,\theta \in R

(i) For  r\in R ,

 (r, \theta)=\begin{Bmatrix}(r, \theta +2 \pi),& \text{ if } \theta < 0 \\(r , \theta-2 \pi),& \text {if } \theta \geq 2\pi\end{Bmatrix}

(ii) For  \theta \in R,(r,\theta)= (-r,\theta+ \pi), \text {if} \quad r < 0

In general,  (r,\theta)= (r,\theta \pm 2n \pi); \quad n\in N

Or  (r,\theta)= (r,\theta +2n\pi); n\in Z

 \implies(r,\theta)= (-r,\theta +(2n+1)\pi), n\in Z

For  (r,\theta)= (-r,\theta +\pi)

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