Step by step
The question
Question: change 30° 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
30° is 30 times one degree.
So we multiply 30 by π/180.
30° = 30 × π180
Top times top: 30π.
The bottom stays 180.
30° = 30π180
3 Make it simpler
30 and 180 can both be divided by 30.
It is the biggest number that goes into both.
30 ÷ 30 is 1.
180 ÷ 30 is 6.
30 ÷ 30 = 1
180 ÷ 30 = 6
So 30° = π/6 radians.
30° = π6
4 Check
Let's check: go back to degrees.
Times 180° over π: the πs cancel.
π6 × 180°π = 180°6 = 30°
We get 30° 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
30° = π6