Value of k for which the point (α, sin -1 α)(α0) lies inside the triangle formed by x+y=k with co-ordinate axes is -

Question

Value of k for which the point (α, sin -1 α)(α>0) lies inside the triangle formed by x+y=k with co-ordinate axes is - (A) (1+(π/2), ∞) (B) (-(1+(π/2)),(1+(π/2))) (C) (-∞, 1+(π/2)) (D) (-1- sin 1,1+ sin 1)

Tardigrade Admin · Accepted Answer

∵ α>0 ⇒(α, sin -1 α) lies in 1 text st quandrant ⇒ k >0 Also the extreme point on the graph of y = sin -1 x is (1, (π/2)) ⇒ 1+(π/2)- k <0 ⇒ k >1+(π/2) ⇒ k ∈(1+(π/2), ∞)

Q. Value of $k$ for which the point $(α, sin^{- 1} α) (α > 0)$ lies inside the triangle formed by $x + y = k$ with co-ordinate axes is -

$(1 + \frac{π}{2}, \infty)$

$(- (1 + \frac{π}{2}), (1 + \frac{π}{2}))$

$(- \infty, 1 + \frac{π}{2})$

$(- 1 - sin 1, 1 + sin 1)$

$∵ α > 0 \Rightarrow (α, sin^{- 1} α)$ lies in $1^{st}$ quandrant $\Rightarrow k > 0$
Also the extreme point on the graph of $y = sin^{- 1} x$ is
$(1, \frac{π}{2})$
$\Rightarrow 1 + \frac{π}{2} - k < 0$
$\Rightarrow k > 1 + \frac{π}{2}$
$\Rightarrow k \in (1 + \frac{π}{2}, \infty)$

Q. Value of k for which the point (α,sin−1α)(α>0) lies inside the triangle formed by x+y=k with co-ordinate axes is -

(1+2π​,∞)

(−(1+2π​),(1+2π​))

(−∞,1+2π​)

(−1−sin1,1+sin1)