# How do you find the angle alpha such that the angle lies in quadrant III and tanalpha=8.000?

The principal value ${\alpha}_{P}$, for $\tan \alpha > 0$ is in the first quadrant. The general value $= n \pi + {\alpha}_{P} , n = 0 , \pm 1 , \pm 2 , \pm 3 ,$..Here, the third quadrant (n=1) value = $\pi + {\alpha}_{P} . = 270 {-}^{o}$
Interestingly, 3-sd (rounded) principal value ${\alpha}_{P}$, for $\tan \alpha = 8000$, is ${90.0}^{o}$.
So, the answer is little short of ${270}^{o}$.