The same turn can be written three ways: a rotating stage platform that turns 1.5 revolutions has swept 540°, and also 3π radians. Converting among the three is one multiply or divide, once you know the linking facts.
One revolution is one full turn: 360°.
One revolution is also 2π radians.
Half a turn links degrees and radians directly: 180° = π radians.
Revolutions to degrees: multiply by 360. Degrees to revolutions: divide by 360.
Revolutions to radians: multiply by 2π. Radians to revolutions: divide by 2π.
Degrees to radians: multiply by π and divide by 180. Radians to degrees: multiply by 180 and divide by π.
π is the calculator's π button, about 3.14159, never a rounded 3.
The stage platform turns 1.5 revolutions. Convert that angular displacement to degrees.
Write down the fact:
1 revolution = 360°
Multiply:
degrees = revolutions × 360
1.5 × 360 = 540
The platform swept 540°.
Convert the platform's 540° to radians.
Write down the fact:
180° = π radians
Divide to count the half-turns, then attach π:
radians = degrees × π / 180
540 × π / 180 = 3π, about 9.42
The platform swept 3π radians, about 9.42 rad.
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