Question

If the point $(2\cos \theta ,2\sin \theta )$, for $\theta \in (0,2\pi )$ lies in the region between the lines $x+y=2$ and $x-y=2$ containing the origin, then $\theta$ lies in

• A. $(0,\frac{\pi }{2})\cup (\frac{3\pi }{2},2\pi )$
• B. $[0,\pi ]$
• C. $(\frac{\pi }{2},\frac{3\pi }{2})$
• D. $[\frac{\pi }{4},\frac{\pi }{2}]$

Answer 1

The correct option is C $(\frac{\pi }{2},\frac{3\pi }{2})$


$P(2\cos \theta ,2\sin \theta )$ lies on the circle $x^2+y^2=4$ on the arc $APB$
Therefore, $\theta \in (\frac{\pi }{2},\frac{3\pi }{2})$