Evaluating a cos graph (image inside)

[thresher]

So with the help from the last question I am finalizing things before finals next week and I am trying to rework this question over and over to see how I can improve my grade on it/where I screwed up. I am attaching a picture of it because of the graph.



I received 6/10 points on this assignment. Here was my work.
with p(t) given and I need to evaluate it at 1000 hares. I just set the equation equal to 1,000 with gave me

1000=1500*cos(pi/60(t-30))+2000. and all of this reduced down to the following in the end

-1000/1500=cos(pi/60(t-30)) followed by

cos^-1(-1000/1500) but clearly I am missing something here as I only received 6/10 and I kinda think that was pitty points >.<

Or should I have done something as simple as following the 1,000 line i drew across the graph and just found where it intersected and get my population from that.

[nona.m.nona]

You were asked for the number of weeks. Perhaps the instructor was looking for numbers useful in real life, including not just the first-period solution(s) but also any solutions shown on the graphed time interval.

[thresher]

Thats kind of what I was thinking too, but I tried reaching him on wednesday and Friday to get clarification with no luck >.< and the paranoid part of me is afraid I will see something similar on a final and not know how to solve it algebraically lol

Breaking things down I get this, -1000=1500cos(pi/60(x-30)) and when I factor pi into everything I get -1000/1500=sin(pix/60)
first I solve for arcsin of -1000/1500 which gives me -41.81 ... but I cant seem to connect where this fits in either.

Also I have the graph traced to weeks 73, 105, 193, and 226.