Posted by sarah on .
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.
Determine the cosine function that results in the same graph as the function above.
Deter

Grade 11 MAth 
Jennifer,
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*(x90))
y = 2.5*sin((x90)/8) 1.5