I'm having a problem understanding exactly why trig functions are defined the way they are. Of course, the definition in terms of 0 to 90 degree angles within right triangles is easy: the functions just give the ratio of the sides given the angle. However, I don't understand how or why trig functions are defined for angles greater than 90 degrees. How does this relate to right angles? Why is it useful to define the trig functions as the points on the unit circle? That definition seems arbitrary, and not useful. Once we go beyond 90 degrees, why is the subject even called trigonometry, if it mostly only relates to the points on the unit circle? Why did we decide to define trig functions this way after defining them as ratios of the sides of right triangles? I hope that somebody can answer these question to put my mind at ease, because as of now, this doesn't make much sense to me.