Answer:
[tex]\sqrt3[/tex]
Step-by-step explanation:
I'm assuming you're dealing with degrees.
If that's the case, then I would first find the closest multiple of 360 to that number.
360*20 = 7200, which is a bit too high; 360*19 = 6840, still a bit too high; 360*18 = 6480, perfect.
Now, just subtract 6480 from 6720 and you will get 240.
The answer is now simplified to tan 240, which can be expressed as sin(240)/cos(240).
240 degrees is 30 degrees away from 270, creating a 30-60-90 triangle.
That means cos(240) is -1/2 and sin(240) is -sqrt(3)/2.
Now, just divide:
[tex]-\frac{\sqrt3}{2}/-\frac{1}{2} = -\frac{\sqrt3}{2}\cdot-2 = \sqrt{3}[/tex]
Therefore, tan(6720 degrees) = [tex]\sqrt3[/tex]
