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. $\left(0, \frac{\pi}{2}\right) \cup \left(\frac{3\pi}{2}, 2\pi\right)$
• B. $\left(0, \pi\right) $
• C. $\left(\frac{\pi}{2}, \frac{3\pi}{2}\right)$
• D. $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$

Answer 1

Answer: (C)

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.
$\therefore \theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$