Question #1:

If cos x = 7/25, and 0 < x < pi/2, what is sin (x - 3pi/2)

question #2:

if tan x = sqrt (3), and 180 (degrees) < x < 270 (degrees), what is sin (x - 210degrees) ?

Try this solution (note, this is not the only way):

Q1: if sin (x - 3pi/2) = -sin (3pi/2 - x) = --cosx=cosx, then sin (x - 3pi/2) = cosx and sin (x - 3pi/2) = 7/25.

Q2: if tan (x) = √3 and x∈ (180°; 270°), then x=arctan√3+180°=60+180=240°.

If x=240°, then sin (x-210°) = sin30°=0.5.