@setlab, in case you haven't revisited your question.
This should help:
http://tutorial.math.lamar.edu/Extras/AlgebraTrigReview/TrigFunctions.aspxI would have done this a little different if I had known this was for a trig class. I'll post the solution later in a format that will be clear, that equation with "t" won't appear like a miracle.
Try this, first some illustrations of three possible solutions; you can see that solution 3 satisfies the problem statement -
Then some illustrations for clarification of the problem -
Then a tabulated example, and the solution -
The key in this solution is to calculate the period, then calculate the angle at a particular time, t. Notice that t/T is simply the fraction of a full cycle at t. That's all there is to the problem.
To calculate the solution for the phase change at the end of the problem, y = -25cos(2pi(t/T) + C), where C is the phase change.
Frankly, I think the problem is a little advanced at that point. The main value of the exercise is to find out whether the student knows the shape of sine and cosine functions, their values at 0 degrees, 90 degrees, and so on, and the sign of the functions in each quadrant of the circle.
On the other hand, if you can reproduce a table similar to the one I show above, calculate the frequency and period, and understand how I arrived at the solution, I'll guess you will be in the top 2% of a trig class.