Step by step
The question
Question: change 360° to radians.
1 Write the rule
Radians are another way to measure an angle.
A half turn is 180°.
In radians, a half turn is π.
So 180° = π.
180° = π
We divide both sides by 180.
One degree is π/180.
1° = π180
Careful!
To get radians, π must end up in the answer.
So π goes on top.
Careful: to radians: × π180
2 Multiply
360° is 360 times one degree.
So we multiply 360 by π/180.
360° = 360 × π180
Top times top: 360π.
The bottom stays 180.
360° = 360π180
3 Make it simpler
360 and 180 can both be divided by 180.
It is the biggest number that goes into both.
360 ÷ 180 is 2.
180 ÷ 180 is 1.
360 ÷ 180 = 2
180 ÷ 180 = 1
So 360° = 2π radians.
360° = 2π
4 Check
Let's check: go back to degrees.
Times 180° over π: the πs cancel.
2π × 180°π = 2 × 180° = 360°
We get 360° again: the angle we started with.
So it is right!
Let's look back.
First: write the rule.
Then: multiply.
Then: make it simpler.
Last: check.
Answer
360° = 2π