Arcs From Degrees
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 21 of 57.
When the angle comes in degrees, convert it first. A bicycle wheel of radius 20 cm turns through 72°. In radians that is 72×π/180, which is 2π/5, so the arc is s = 20×2π/5, which is 8π cm, about 25.13 cm.
The same answer comes from fractions of the circle. 72° is 72/360, a fifth, of a turn, so the arc is a fifth of the circumference 40π: again 8π. Both routes say the same thing; the formula just saves writing.
The trap is skipping the conversion: 20 × 72 = 1440 cm, more than eleven times the whole circumference.
Challenge
A car's windscreen wiper is 45 cm long and sweeps through 110°. How far does its tip travel in one sweep, in cm? On the blank board, write s with the numbers in, then a line with s rounded to one decimal place. Then press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Angles and the Unit Circle
1A Point on a Circle
Height on the CircleAcross: the CosineSame Height, Two AnglesRecap: Height and Across4Radians
What a Radian IsDegrees to RadiansRadians to DegreesRadians Without πTurns in RadiansRecap: Radians5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza