(Angle measure and unit nature)
a. (i) Define one radian. Explain briefly why the radian is regarded as a dimensionless unit.
b. (ii) Using the definition of radian, derive the relation between the radian measure θ and the degree measure D of the same angle.
c. (iii) Hence, convert 65π radians into degrees.
(a) Give your answer correct to one decimal place in decimal degrees.
(b) Express the same result in degrees–minutes–seconds (DMS) form, correct to the nearest second.