Question

Find the set of values of `alpha` in the interval [ `pi/2,3pi/2`], for which the point (`sin alpha, cos alpha`)does not exist outside the parabola `2 y^2 + x - 2 = 0`
A. `[pi//2, 5pi//6]`
B. `[pi, 3pi//2]`
C. `[pi//2, 5pi//6]uu[pi,3pi//2]`
D. `[5pi//6, 3pi//2]`

Answer 1

Correct Answer - C
If the point (sin `alpha`, cos `alpha`) lies inside or on the parabola `2y^(2)+x-2=0`, then
`2 cos^(2)alpha+sinalpha-2le0`
`rArr" "2-2sin^(2)alpha+sinalpha-2le0`
`rArr" "sin alpha(2 sin^(2)alpha-1)ge0`
`rArr" "sinalphale(2 sinalpha-1)ge0`
`rArr" "alphain[pi,3pi//2]or, alphain[pi//2,5pi//6]`
`rArr" "alphain[pi//2, 5pi//6]uu[pi,3pi//2]`