If the point (2 cos θ, 2 sin θ) for 0 ∈(0,2 π) lies in the region between the lines x+y=2 and x-y=2 containing the origin, then θ lies in

Question

If the point (2 cos θ, 2 sin θ) for 0 ∈(0,2 π) lies in the region between the lines x+y=2 and x-y=2 containing the origin, then θ lies in (A) (0, (π/2)) ∪ ((3π/2), 2π) (B) (0, π)  (C) ((π/2), (3π/2)) (D) ((π/4), (π/2))

Tardigrade Admin · Accepted Answer

Given that (2 cos θ, 2 sin θ) will lie on the circle x2+y2=4 (from the given figure), Since, point lies on the region containing origin. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e61f499f0c23f97db4bd39247342aeca-.png" /> So, point will be on the shaded region. ∴ θ ∈((π/2), (3 π/2))

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

$(0, \frac{π}{2}) \cup (\frac{3 π}{2}, 2 π)$

$(0, π)$

$(\frac{π}{2}, \frac{3 π}{2})$

$(\frac{π}{4}, \frac{π}{2})$

Given that $(2 cos θ, 2 sin θ)$ 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.
$∴ θ \in (\frac{π}{2}, \frac{3 π}{2})$

Q. If the point (2cosθ,2sinθ) for 0∈(0,2π) lies in the region between the lines x+y=2 and x−y=2 containing the origin, then θ lies in

(0,2π​)∪(23π​,2π)

(0,π)

(2π​,23π​)

(4π​,2π​)