SOLUTION: a) Determine the equation of a sine function that would have a range of {y ER|-4≤y≤1} and a period of 45 degrees. b) Determine the cosine function that results in the same g

Algebra ->  Finance -> SOLUTION: a) Determine the equation of a sine function that would have a range of {y ER|-4≤y≤1} and a period of 45 degrees. b) Determine the cosine function that results in the same g      Log On


   

Question 1141502: a) Determine the equation of a sine function that would have a range of {y ER|-4≤y≤1}
and a period of 45 degrees.
b) Determine the cosine function that results in the same graph as the function in part (a).
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
a) Determine the equation of a sine function 
y=Asin%28Bx%2BC%29%2BD

that would have a range of {y ER|-4≤y≤1}
 
I don't understand "ER", so I'll assume the range is{y|-4≤y≤1}

The range is from -4 to 1, a span of 1-(-4)=1+4=5 units. So we know it is a
downward shifted sine function that has an amplitude of half of 5 which is
5/2, so A = 5/2.  Also, it must be shifted downward so that the horizontal
axis of symmetry is shifted from the x-axis down to halfway between -4 an 1,
which is %28-4%2B1%29%2F2=-3%2F2, so D+=+-3%2F2. So we have:

y=expr%285%2F2%29sin%28Bx%2BC%29-3%2F2

and a period of 45 degrees.

The period is given by %28360%5Eo%29%2FB so 360%5Eo%2FB=45%5E%22o%22

B%2A45%5E%22o%22=360%5Eo

B=360%5Eo%2F45%5Eo

B=8, so we have:

y=expr%285%2F2%29sin%288x%2BC%29-3%2F2

and we may as well take C=0 since there is no need for any horizontal shift.

So an answer is:

y=expr%285%2F2%29sin%288x%29-3%2F2

The graph one one period (from 0° to 45° is:
b) Determine the cosine function that results in the same graph as the function in part (a).

Use the identity sin%28theta%29=cos%28theta-90%5Eo%29

y=expr%285%2F2%29cos%288x-90%5Eo%29-3%2F2

Edwin