Calculate tan^-1(√3/3) in degrees

Step by step

The question

Question: find tan⁻¹(√3/3).

Give the angle in degrees.

1 What it asks

tan⁻¹ of √3/3 means: the angle whose tangent is √3/3.

We call that angle θ.

So tan θ = √3/3.

2 The allowed range

Many angles have a tangent of √3/3.

210° and 390° work too.

The tan⁻¹ button must give just one.

So tan⁻¹ gives an angle between −90° and 90°: the right half of the circle.

Not −90° or 90° themselves: tan has no value there.

3 Find the angle

From the unit circle: tan 30° = √3/3.

Careful!

Other angles have the same tan, like 210°.

But only 30° is in the range.

So the button gives 30°.

30° is in the range.

So θ = 30°.

So tan⁻¹(√3/3) = 30°.

4 Check

Let's check: tan 30° is √3/3.

And 30° is inside the range.

So it is right!

Let's look back.

First: what it asks.

Then: the allowed range.

Then: find the angle.

Last: check.