Question

What is the value of `tan((19pi)/3)`?

Answer 1

`tan((19pi)/3)=sqrt3=1.732`

Explanation:

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

As `tan((19pi)/3)=tan((18pi+pi)/3)=tan(6pi+pi/3)=tan(pi/3)`

(as `6pi` is a multiple of `pi` which is cycle for function tan)

and as `tan(pi/3)=sqrt3`, we have

`tan((19pi)/3)=sqrt3=1.732`