Calculate tan^-1(√3)

Step by step

The question

Question: find tan⁻¹(√3).

1 What it asks

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

We call that angle θ.

So tan θ = √3.

2 The allowed range

Many angles have a tangent of √3.

240° and 420° 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 60° = √3.

Careful!

Other angles have the same tan, like 240°.

But only 60° is in the range.

So the button gives 60°.

60° is in the range.

So θ = 60°.

4 In radians

In radians: 60 times π over 180.

That is π/3.

So tan⁻¹(√3) = 60° = π/3.

5 Check

Let's check: tan 60° is √3.

And 60° is inside the range.

So it is right!

Let's look back.

First: what it asks.

Then: the allowed range.

Then: find the angle.

Then: in radians.

Last: check.