Step by step
The question
Question: change 210° 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
210° is 210 times one degree.
So we multiply 210 by π/180.
210° = 210 × π180
Top times top: 210π.
The bottom stays 180.
210° = 210π180
3 Make it simpler
210 and 180 can both be divided by 30.
It is the biggest number that goes into both.
210 ÷ 30 is 7.
180 ÷ 30 is 6.
210 ÷ 30 = 7
180 ÷ 30 = 6
So 210° = 7π/6 radians.
210° = 7π6
4 Check
Let's check: go back to degrees.
Times 180° over π: the πs cancel.
7π6 × 180°π = 7 × 180°6 = 210°
We get 210° 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
210° = 7π6