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

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Answer 1 · 2016-06-30T15:58:56

#Arctan (1/sqrt3) = 30° or 210°#

The sides of length #1 and sqrt3# 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 #sqrt3# 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 #"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°#