# What is #Arctan (-1/3 * sqrt3)#?

##### 2 Answers

#### Explanation:

We need to remember what the tan is. See the following two right triangles:

and

These two angles are the same since

Pytagoras says that the hypotenuse squares is the sum of the square of the sides, i.e.

Therefore

That means

Hopefully you remember that in an equilateral triangle all sides are equal, and that each angle is

Here

This means that

Except that we have been working with positive values, so

#### Explanation:

There are really very few non-trivial trig function values that student is expected to have at their fingertips. Besides the multiples of

We hopefully can already recognize

Now we learn the tangents.

That's pretty close to the one we need for this problem; let's enumerate the others.

Complementary angles have reciprocal tangents.

OK, we learned to recognize

So,

The general solution to

That's