Step by step
The question
Question: change 450° 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
450° is 450 times one degree.
So we multiply 450 by π/180.
450° = 450 × π180
Top times top: 450π.
The bottom stays 180.
450° = 450π180
3 Make it simpler
450 and 180 can both be divided by 90.
It is the biggest number that goes into both.
450 ÷ 90 is 5.
180 ÷ 90 is 2.
450 ÷ 90 = 5
180 ÷ 90 = 2
So 450° = 5π/2 radians.
450° = 5π2
4 Check
Let's check: go back to degrees.
Times 180° over π: the πs cancel.
5π2 × 180°π = 5 × 180°2 = 450°
We get 450° 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
450° = 5π2