Graphing Cosine Curve

[Zfuss12]

I have recently been studying for my Math B regents, a new york stanadardized test and came across this problem, Im not quite familiar with graphing cosine curves so any help would be greatly appreciated.

The enrollment at a particular private school runs in cycles. Over a ten-year period, the enrollment has a range of 300 to 600 students. Sketch a possible cosine curve that would illustrate this cyclic pattern and write the equation.

 

[daon]

I have recently been studying for my Math B regents, a new york stanadardized test and came across this problem, Im not quite familiar with graphing cosine curves so any help would be greatly appreciated.

The enrollment at a particular private school runs in cycles. Over a ten-year period, the enrollment has a range of 300 to 600 students. Sketch a possible cosine curve that would illustrate this cyclic pattern and write the equation.

Aplitude (A) = half the difference of the lowest point and the highest point.
In this case, A = 1/2(600-300) = 150

"Over a ten-year period" I assume means that every ten years the "cyclic pattern" repeats itself, so I will say the period = 10.

The normal period of cosine is 2pi, and given the cosine equation ACos(Bx + C), the period is given by 2pi/B, so set 2pi/B = 10, we get B = pi/5.

So our cosine curve is ACos(Bx + C), (but C is zero) = 150Cos([pi/5]x). EXCEPT, that this will give a cosine curve ranging from -150 to +150, we need a curve going from 300 to 600, so add a vertical shift of 450:

150Cos([pi/5]x) + 450

 

[Zfuss12]

Thanks alot......you have been a great help