Question

If $(x,y)$ be the Cartesian coordinates of the point whose polar coordinates are $(\sqrt{2},\frac{\pi }{2})$, then the value of $x^4+y^4$ is

Answer 1

$(r,\theta )\equiv (\sqrt{2},\frac{\pi }{2})$
$\because x=r\cos \theta$
$y=r\sin \theta$
$\therefore x=\sqrt{2}\cos \frac{\pi }{2}$ and $y=\sqrt{2}\sin \frac{\pi }{2}$
$\Rightarrow x=0$ and $y=\sqrt{2}$
$\therefore x^4+y^4=4$