# How do you find the exact value of arctan((1/sqrt3)?

Jun 30, 2016

Arctan (1/sqrt3) = 30° or 210°

#### Explanation:

The sides of length $1 \mathmr{and} \sqrt{3}$ are found in the special triangle with angles 30° and 60°.

The base is 1, next to the angle of 60° while the altitude is $\sqrt{3}$ and the the hypotenuse is 2. The angle of 30° is at the top of the triangle.

We have been given a ratio and asked for an angle. (arctan)
The Tan ratio is $\text{opposite"/"adjacent}$

Therefore the angle being referred to is the 30° angle.

Arctan (1/sqrt3) = 30°

However, as the value is positive, this could apply to an angle in the 3rd quadrant as well.

180°+30° = 210°