BQ#5: Unit T Concepts 1-3

Whenever you have 0 in your denominator it will be undefined. You can only have an asymptote if you have an undefined number. All the trig functions have a ratio:

Sine               Cosine                  Cosecant                   Secant                  Tangent                Cotangent

      y/r                    x/r                           r/y                           r/x                         y/x                         x/y

When we are talking about the Unit Circle "r" matter what it equal to 1. When we look at the ratios, sine and cosine are the only trig functions where r is the denominator. This means no matter what the numerator is, the function will never be undefined because the denominator will always be 1. All the other functions have the possibility of being undefined because x or y can equal to 1 or 0 and that all depends on what point on the graph you are on. If you are on 0 or 180 or 360 degrees, cosecant and cotangent will be 0 because the ordered pairs on that point are (1,0) and 0 is y. If you are on 90 or 270 degrees, secant and tangent will be 0 because the ordered pairs are (0,1) and x is 0.