M5.3.1 For the adult
Radians
Is there a better way to measure an angle than in degrees?
What this chapter teaches
A radian is the angle at the centre of a circle that cuts off an arc as long as the radius. A half turn is π radians (180°) and a full turn is 2π radians. In radians, the arc is s = rθ and the sector area is ½r²θ. Those formulas fail if the angle is in degrees, and a calculator must be in radian mode.
Three questions to ask
There is no one right wording. Listen for the idea.
- How many radii of string go round a whole circle?
- Why does a sector with radius 4 cm and angle 60° not have an arc of 240 cm?
- What is the perimeter of a sector, and why is it more than the arc?
After the chapter, the learner can
- Change between degrees and radians
- Find arc length and sector area using radians
What they copy into their notebook
π rad = 180°. Degrees to radians: × π/180. Radians to degrees: × 180/π. s = rθ, A = ½r²θ, perimeter 2r + rθ. Radians only. Calculator in RAD mode.