If the polar coordinates of a point are left( | vedclass

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Question

(A) The relationship between polar coordinates $(r, 	heta)$ and Cartesian coordinates $(x, y)$ is given by $x = r \cos 	heta$ and $y = r \sin 	heta

Vedclass · Accepted Answer

$(\sqrt{2}, \sqrt{2})$

Vedclass · Answer

(A) The relationship between polar coordinates $(r, 	heta)$ and Cartesian coordinates $(x, y)$ is given by $x = r \cos 	heta$ and $y = r \sin 	heta$. Given $r = 2$ and $	heta = \frac{\pi}{4}$. $x = 2 \cos \left(\frac{\pi}{4}ight) = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2}$. $y = 2 \sin \left(\frac{\pi}{4}ight) = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2}$. Thus,the Cartesian coordinates are $(\sqrt{2}, \sqrt{2})$.

If the polar coordinates of a point are $\left(2, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

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