Verified answer

180° ≤ x ≤ 270° => 3rd. quadrant,

sec x = -√10 =>cos x = -1/√10

draw a right triangle @ 3rd. quadrant, if hypotenuse is √10, adjacent is -1, then the

opposite will be -3

sin x = -3/√10

sin(2x) = 2sin x cos x = 2*(-3/√10)(-1/√10) = 3/5

cos(x/2) = -√[(1+cosx)/2] => take negative, because x/2 be 2nd.quadrant, cosines negative.

= -√[(1 - 1/√10 )/2]

formula:

sin(x/2) = ±√[(1-cosx)/2]

cos(x/2) = ±√[(1+cosx)/2]

tan(x/2) = sinx / (1+cosx)