Step by step
The question
Question: change −120° 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
−120° is −120 times one degree.
So we multiply −120 by π/180.
−120° = −120 × π180
Top times top: 120π.
The bottom stays 180.
−120° = −120π180
3 Make it simpler
120 and 180 can both be divided by 60.
It is the biggest number that goes into both.
120 ÷ 60 is 2.
180 ÷ 60 is 3.
120 ÷ 60 = 2
180 ÷ 60 = 3
So −120° = −2π/3 radians.
−120° = −2π3
4 Check
Let's check: go back to degrees.
Times 180° over π: the πs cancel.
−2π3 × 180°π = −2 × 180°3 = −120°
We get −120° 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
−120° = −2π3