Question

What is the value of the expression? Do not use a calculator.

tan(-11pi/6)

Answer 1

`tan((-11\pi)/(6))= tan (-\pi +(-5\pi)/(6))\\\\ tan[-(\pi +(5\pi)/(6))]\\\\=-tan(\pi +(5\pi)/(6))\\\\=-(tan(5\pi)/(6))\\\\=-tan((5\pi)/(6))\\\\=-tan(\pi -(\pi)/(6))\\\\=tan (\pi)/(6)\\\\ =(1)/(√(3))`

Answer 2

tan(-11π/6)
= tan(π/6 - 2π)
= tan(π/6)
= √(3)/3