Step by step
The question
Question: solve 2 cos x = √3.
Find every angle from 0° up to 360°.
We want the angles from 0° to 360°: one full turn.
1 Remove the 2
2 cos x means 2 times cos x.
We want just cos 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 divided by 2 is 1.
So just cos x is left.
So cos x = √3/2.
2 Find the reference angle
From the unit circle: cos 30° = √3/2.
So the reference angle is 30°.
3 Find every angle
Cos is the across value.
The points with the across value we want are on an up-and-down line.
Cos is positive right of the y-axis: quadrants I and IV.
30° and 360° − 30°: x = 30° or 330°.
On the circle: 2 points, so 2 angles.
So x = 30°, 330°.
4 Check
Let's check every answer in the equation.
Each one must give √3.
Every answer works.
So x = 30°, 330°.
Let's look back.
First: remove the 2.
Then: find the reference angle.
Then: find every angle.
Last: check.