**Answer:**

tan(19π/3)=√3=1.732

**Explanation:**

Every trigonometric function has a cycle of 2π, i.e. after 2π, the function is repeated. In fact functions **tan** and **cot** repeat after every π.

As tan(19π/3)=tan[(18π+π)/3]=tan(6π+π/3)=tan(π/3)

(as 6π is a multiple of π which is cycle for function **tan**)

and as tan(π/3)=√3, we have

tan(19π/3)=√3=1.732