Question

The price of Trigonometry Stock varies sinusoidally with time. At the start of this year, the price of the stock was 110$ per share. Over the next 3 days, the price climbs to a peak of 120$ per share. If the lowest price the stock reaches is 80$ per share, how much money can you make this year (in 365 days starting from the start of this year) if you begin with 1000$ and time all of your trades perfectly?(Assume you can buy fractions of a share of stock, and that you can buy stock as many times as you want, but can never sell stock you haven't already bought first.) 

This is the questions, and I need help finding the function because I don't know the period of this function. 

I'd appreciate the help :D

Answer 1

let the price of stock be represented by equation
stock(t)=Asin (kt)+c
at t=0 c=110
stock(t)=Asin(kt)+110
at t=3  120=Asin(3k)+110
A=10/sin(3k)
the lowest value is 80
c-A=80
110-A=80
A=30
so sin 3k=1/3
k=6.49 degrees/days
for 365 days t=365days
so we have integrate from 0 to 52.143 weeks and then add 1000 to it
stock(t)=30sin(6.49t)+110
now integrate 
$I= \int\limits^{365}_{0} {30sin(6.49t)+110} \, dt=40150.01835254824$
add 1000+40150.01835254824=41150.01835254824 
HOPE THIS HELPS!