(D) The relation between polar coordinates $(r, \theta)$ and Cartesian coordinates $(x, y)$ is given by $x = r \cos \theta$ and $y = r \sin \theta$. G

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(D) The relation between polar coordinates $(r, \theta)$ and Cartesian coordinates $(x, y)$ is given by $x = r \cos \theta$ and $y = r \sin \theta$. Given $r = \sqrt{2}$ and $\theta = \frac{\pi}{4}$. $x = \sqrt{2} \cos \left(\frac{\pi}{4}\right) = \sqrt{2} \times \frac{1}{\sqrt{2}} = 1$. $y = \sqrt{2} \sin \left(\frac{\pi}{4}\right) = \sqrt{2} \times \frac{1}{\sqrt{2}} = 1$. Therefore,the Cartesian coordinates are $(1, 1)$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

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

MHT CET 2021 All MHT CET

A
$(\sqrt{2}, 2)$
B
$(1, -1)$
C
$(2, \sqrt{2})$
D
$(1, 1)$

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