mathematics Module
Interactive Simulation Screen
SYS_OKLesson Directive // Angle WorkshopREF_CORE
Degrees vs Radians
Hover over a variable in the formula above, or see glossary below:
Arc Length
m
Radius
m
Angle (Radians)
rad
While degrees (360 in a circle) are common, mathematicians prefer radians. A radian is the angle created when the arc length equals the radius. A full circle is 2π radians.
INSIGHT: Radians directly relate the angle to the physical distance around the circle.
Arc Length
If you know the radius of a circle and the central angle in radians, the arc length is simply their product.
INSIGHT: This formula only works if the angle is in radians!
Sector Area
The area of the "slice of pie" (sector) is given by A = (1/2) * r² * θ. This is directly derived from the area of a full circle.
INSIGHT: Sector area scales quadratically with radius but linearly with the angle.