$4.$ The distance from the Sun can be approximated by the equation:

D $=2\mathrm{.}5$ cos $[0\mathrm{.}0172($n $-185)]+150,$ where D represents the distance in

millions of kilometres and n represents the number of days into the year.

$(1$ mark$)$ a$.$ How far will Earth be from the Sun on March $21,$ the eightieth day of the year?

$(1$ mark$)$ b$.$ Determine the range of distances that Earth can be from the Sun.

$(2$ marks$)$ c$.$ What is the period length of this cycle? Explain what the period length means in the

context of this question.