Math
posted by David .
cot (theta)=9/8, cos (theta)<0

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