cot (theta)=-9/8, cos (theta)<0

Answer 1

Are we solving for theta ??

if so, then
tan Ø = -8/9 and if cos Ø < 0
Ø must be in quadrant II

angle in standard position is 41.63°
( since tan 41.63° = +.888889 or 8/9 )

so Ø = 180 - 41.63 or 138.37°

check:
tan 138.37 = -.888889
cos 138.37 is negative.

Change your calculator to Radians if you want those units