Question

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

• A. $(\theta ,\frac{\pi }{2})\cup (\frac{3\pi }{2},2\pi )$
• 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 $(\frac{\pi }{2},\frac{3\pi }{2})$

Given that $(2\cos \theta ,2\sin \theta )$ will lie on the circle $x^2+y^2=4$ (from the given figure). Since point lies on the region containing origin.
So, point will be on the shaded region.
$\therefore \theta \in (\frac{\pi }{2},\frac{3\pi }{2})$