Verified answer

so in Q2 , x is negative and y is positive

so , cos is negative and sin is positive

cos(theta) = +/- √(1 - sin^2(theta)

but here , we need the -

cos(theta) = - √( 1- sin^2(theta) ) = - sqrt (1 - ( 2*√(5)/5)^2 )

cos(theta) = - √(1 - 4*5/25) = -√( 25/25 - 20/25) = -√(5/25) = -√(5)/5

cos(theta) = -√(5)/5

sin²∅ + cos²∅ = 1

4 /5 + cos²∅ = 1

cos²∅ = 1/5

cos ∅ = - 1/√5_______3rd quadrant