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

Relation between Cartesian & Polar Coordinates

If  P(r,\theta) = P(x,y),  then by definition of sine and cosine functions,

 x=r\cos\theta\quad \text { and }\quad y=r\sin\theta

Hence, (r,\theta) \text { and }  (x,y) are respectively polar and cartesian coordinates of the point  P

(i)  \sin\theta=0\Rightarrow \theta=n\pi , where  n is an integer.

(ii)  \cos\theta=0\Rightarrow \theta=(2n+1)\dfrac{\pi}{2}, \text { where } n\in Z .

(iii)  \csc\theta=\dfrac{1}{\sin\theta},\quad \theta\neq n\pi,  n\in Z

(iv)  \sec\theta=\dfrac{1}{\cos\theta}, \quad \theta\neq (2n+1)\dfrac{\pi}{2}, n\in Z

(v)  \tan\theta=\dfrac{\sin\theta}{\cos\theta}, \quad \theta\neq (2n+1)\dfrac{\pi}{2}, \quad n\in Z

(vi) \cot\theta=\dfrac{\cos\theta}{\sin\theta}, \quad \theta\neq n\pi,\quad n\in Z

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