Key Idea: A radian is another unit for angles. With angles in radians, the arc and sector formulas are short, so you can find lengths and areas of curved parts, like the area a sprinkler waters.
| Task | Formula |
|---|---|
| Degrees to radians | × π/180 |
| Radians to degrees | × 180/π |
| Arc length | l = rθ |
| Sector area | A = ½r²θ |
Common slips
- Both formulas need θ in radians. Convert degrees first.
- Arc length multiplies r and θ. Do not add them.
- Square the radius before halving, and keep the ½.
- Interpret the answer, for example whether the sprinkler covers the lawn.
Set your GDC to radian mode before any arc or sector question.
Convert 90° to radians. π/2.
A sector has r = 8 m and θ = 1.2. Find its area. ½(64)(1.2) = 38.4 m².
Does that sprinkler water all of a lawn 8 m by 8 m? No. It covers 38.4 of 64 m², about 60%.
Find the arc length when r = 5 cm and θ = 2. 10 cm.