Determine the equation of a sine function that would have a range of {y| -4 ≤ y ≤ 1, y ε R} and a period of 45o.

Question

Determine the cosine function that results in the same graph as the function above.
Deter

Answer 1

The midpoint of the range -4 <= y <=1 is y = -1.5 with an amplitude of 2.5

The equation is now of the form:

y = 2.5*sin(a*x) - 1.5

When a = 1, the period is 360 degrees. So when a = 45/360; the period will be 45 degrees, or when a = 1/8

y = 2.5*sin(x/8) - 1.5

for the second part, note that sin(a*x) = cos(a*(x-90))

y = 2.5*sin((x-90)/8) -1.5