We can use the sine, cosine, and tangent functions to talk about some new trigonometric functions: cosecant, secant, and cotangent.

Cosecant is the reciprocal function of sine. This means that  . On a right triangle, we can identify the trigonometric ratio  . We can use this information to create a graph of  . The graph will have an asymptote any time  . We also know that   any time  ,   any time  , and has the same period as . Here is the graph of  :

Secant is the reciprocal function of cosine. This means that  . On a right triangle, we can identify the trigonometric ratio  . We can use this information to create a graph of  . The graph will have an asymptote any time  . We also know that   any time  ,   any time  , and has the same period as . Here is the graph of  :

Cotangent is the reciprocal function of tangent. This means that  . On a right triangle, we can identify the trigonometric ratio  . We can use this information to create a graph of  . The the graph will have an asymptote any time  , and it will have a value of 0 any time  has an asymptote. We also know that   any time  ,   any time  , and has the same period as . Here is the graph of  :