What is the exact trigonometric function value of tan 2670 degrees?

First start by reducing 2,670 down to be greater than 0 but less than 360.

We can find co-terminal angles to 2,670 by subtracting 360:

2,670-360=2,310

2,310-360=1,950

1,950-360=1,590

1,590-360=1,230

1,230-360=870

870-360=510

510-360=150

So, now the problem is Tan(150).

This is equal to the Sin(150)/Cos(150). The Sin(150)=1/2 and Cos(150)=-sqrt(3)/2

So Sin(150)/Cos(150)=[1/2]/[-sqrt(3)/2]=[1/2]*[2/-sqrt(3)]=-1/sqrt(3)=-sqrt(3)/3

So Tan(2,670)=-sqrt(3)/3 ("Negative square root of three over three")