Question

Find the value of tan 6720 with out calculator

Answer 1

The best thing I can say is use a online scientific calculator.

Answer 2

Answer:

$\sqrt3$

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:

$-\frac{\sqrt3}{2}/-\frac{1}{2} = -\frac{\sqrt3}{2}\cdot-2 = \sqrt{3}$

Therefore, tan(6720 degrees) = $\sqrt3$