trig formula for a population

The population, *P*, of a certain type of bird on a remote island varies during the course of a year according to feeding, breeding, migratory seasons and predator interactions. An ornithologist doing research into bird numbers for this species attempts to model the population on the island with the annually periodic equation

*P = N* – *C*cos*wt*°

Where *N*, *C *and* w* are constants, and *t *is the time in weeks, with *t *= 0 representing midnight on the first of January.

a. Taking the period of this function to be 50 weeks, find the value of *w.*

b. Use the equation to describe, in terms of *N *and* C*,

(i) the number of birds of this species on the island at the start of each year;

(ii) the maximum number of these birds, and the time of year when this occurs

My answers were

a. *w=*7.2

b. (i) P=N-C

These were correct

For b. (ii) I gave

P=N+C, t=25 weeks

However the answer is P=N+C for t=37.5 weeks.

How is this possible?

P=N+C when cos*wt*°=-1, therefore when *t= *(arcos(-1))/*w *= 180/7.2 = 25

…?

Re: trig formula for a population

with the function given, max occurs at t = T/2 ... the "answer" is incorrect.

an aside ... what is the source of these problems? reason I ask is that most times problems that model trig functions use radians rather than degrees.

Re: trig formula for a population

A level mathematics for Cambridge International Examinations, Pure Mathematics 1