Equipped with Identities (5-32) - (5-35), we can now establish many other properties of the trigonometric functions.  We begin with some periodic results.  For all complex numbers ,  

                 

Clearly, .  By Identity (5-34) this expression is  

               

Again, the proofs for the other periodic results are left as exercises.

Exploration for trigonometric identities.

(c) 2006 John H. Mathews, Russell W. Howell