Solve 3 tan x = √3 Step by Step

Step by step

The question

Question: solve 3 tan x = √3.

Find every angle from 0° up to 360°.

3 tan x = √3

We want the angles from 0° to 360°: one full turn.

0° ≤ x < 360°

1 Remove the 3

3 tan x means 3 times tan x.

We want just tan x.

To remove times 3, we divide by 3.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

3 tan x3 = √33

3 divided by 3 is 1.

So just tan x is left.

So tan x = √3/3.

tan x = √33

2 Find the reference angle

From the unit circle: tan 30° = √3/3.

So the reference angle is 30°.

tan 30° = √33

3 Find every angle

Tan is positive in quadrants I and III.

30° and 180° + 30°: x = 30° or 210°.

tan x = √33: x = 30° or 210°

On the circle: 2 points, so 2 angles.

So x = 30°, 210°.

x = 30°, 210°

4 Check

Let's check every answer in the equation.

Each one must give √3.

x = 30°: 3 tan 30° = 3 × √33 = √3

x = 210°: 3 tan 210° = 3 × √33 = √3

Every answer works.

So x = 30°, 210°.

Let's look back.

First: remove the 3.

Then: find the reference angle.

Then: find every angle.

Last: check.

Answer