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

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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(20065)   (Show Source): You can put this solution on YOUR website!
a) Determine the equation of a sine function

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 , so . So we have:



and a period of 45 degrees.

The period is given by  so 





, so we have:



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

So an answer is:



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 



Edwin
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