secant math word problem

Question

Given  where ,  determine the related acute angle and all possible principal angles to the nearest degree. 

Answer 1

secT = -1.25 = -5/4

cosT = 1/T = -4/5= -.8, T = cos^-1(-.8) = 143.13 degrees in quadrant II

but also in quadrant III

T= 216.87 degrees

180 +/- 36.87

= 143.13 or 216.87

but neither is acute, so there is no solution

reference angle though is 36.87 degrees, rounded off, which is in quadrant I and an acute angle