Step by step
The question
Question: change 45° 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
45° is 45 times one degree.
So we multiply 45 by π/180.
45° = 45 × π180
Top times top: 45π.
The bottom stays 180.
45° = 45π180
3 Make it simpler
45 and 180 can both be divided by 45.
It is the biggest number that goes into both.
45 ÷ 45 is 1.
180 ÷ 45 is 4.
45 ÷ 45 = 1
180 ÷ 45 = 4
So 45° = π/4 radians.
45° = π4
4 Check
Let's check: go back to degrees.
Times 180° over π: the πs cancel.
π4 × 180°π = 180°4 = 45°
We get 45° 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
45° = π4