Okay so Im reading a book on analytic geometry because my algebra class is starting to really bore me, and I ran across this: slope = m = -1/2 (easy enouph) but then it states "since the slope is the tangent of the angle of inclination θ, we have: tan θ = -1/2 okay so I guess my first question is: What is a tangent in analytic geometry? continuing with my story: the very next thing it gives my is the angle of inclination So for this it goes: θ = tan^-1 (-1/2) = 153°26'. What the heck? Can someone explain this problem above in greater detail. I know that tan^-1 is the inverse of tan but without understanding what tangent actually is that doesnt help me much. Also, how do you calculate this to get the answer? I have looked at a ton of online sources but cant seem to find any answers to my questions.