Solve 2 sin x = √3 Step by Step

Step by step

The question

Question: solve 2 sin x = √3.

Find every angle from 0° up to 360°.

2 sin x = √3

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

0° ≤ x < 360°

1 Remove the 2

2 sin x means 2 times sin x.

We want just sin x.

To remove times 2, we divide by 2.

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.

2 sin x2 = √32

2 divided by 2 is 1.

So just sin x is left.

So sin x = √3/2.

sin x = √32

2 Find the reference angle

From the unit circle: sin 60° = √3/2.

So the reference angle is 60°.

sin 60° = √32

3 Find every angle

Sin is the up value.

The points with the height we want are on a flat line.

Sin is positive above the x-axis: quadrants I and II.

60° and 180° − 60°: x = 60° or 120°.

sin x = √32: x = 60° or 120°

On the circle: 2 points, so 2 angles.

So x = 60°, 120°.

x = 60°, 120°

4 Check

Let's check every answer in the equation.

Each one must give √3.

x = 60°: 2 sin 60° = 2 × √32 = √3

x = 120°: 2 sin 120° = 2 × √32 = √3

Every answer works.

So x = 60°, 120°.

Let's look back.

First: remove the 2.

Then: find the reference angle.

Then: find every angle.

Last: check.

Answer