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Central angle: ΞΈ=s/r where ΞΈ is in radians

When you are dividing s by r to obtain ΞΈ , s and r must have the same units. The units cancel leaving ΞΈ as a dimensionless ratio of two lengths. Thus, the radian is not a unit of measure like the degree or inch, although we usually carry it along as if it were.

Q1. Find the radius of a circle in which an angle of 2.06 radians

intercepts an arc length of 115 m.

Q2. How many kilometers (arc length) north of the equator is a town of latitude 43.60 N. Assume that the earth is a sphere of radius 6370 km.

Recall: Latitude is the angle (measured at the earthβs center) between a point on the earth and the equator. Longitude is the angle between the meridian passing through a point on the earth and the principal (or prime) meridian passing through Greenwich, England.

Q3. If we assume the earth’s orbit around the sun to be circular, with a radius of 150 million km, how many kilometres (arc length) does the earth travel (around the sun) in 125 days?

Video “π How to find the central angle of the arc length (Part 2)” Author: Study Force