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

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

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

Medium

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

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

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