Sinusoid question HELP

[Snicho1]

This question is in one of my assignments, and im having difficulty with determining the alpha value (the starting point) and whether or not it has a p value (2(pi)/b)). Ive worked out the Amplitude as 3 and the Mean value as 4, so my equation so far is y=4+3sin(x), im just not sure how to get the other bits. So heres the question, guidance/help would be greatly appreciated!!!

A variable y is oscillating sinusoidally in a 24 hour cycle. It reaches its maximum value of 7 at 9am every morning, and its minimum value of 1 at 9pm
every night. Find a formula for y as a function of t (measured in hours), given that it is midnight when t = 0.

Thank you!

 

[daon2]

The function will be equal to its "mean" value at quarter of its period before (or after) its maximum (or minimum).

 

[Deleted member 4993]

This question is in one of my assignments, and im having difficulty with determining the alpha value (the starting point) and whether or not it has a p value (2(pi)/b)). Ive worked out the Amplitude as 3 and the Mean value as 4, so my equation so far is y=4+3sin(x), im just not sure how to get the other bits. So heres the question, guidance/help would be greatly appreciated!!!

A variable y is oscillating sinusoidally in a 24 hour cycle. It reaches its maximum value of 7 at 9am every morning, and its minimum value of 1 at 9pm
every night. Find a formula for y as a function of t (measured in hours), given that it is midnight when t = 0.

Thank you!

when t=9, y is maximum so x = π/2

and at t = 21, y is minimum so x = 3π/2

thus (we x is a linear function of t)

(t - 9)/(21-9) = (x - π/2)/(3π/2 - π/2)

π(t-9)/12 = x - π/2

x = tπ/12 -π/4

and continue........