On a certain spring day with 12 hours of daylight, the light intensity i takes on its largest value of 610 calories/cm^2 at midday. if t = 0 corresponds to sunrise, find a formula i = a sin bt, where t is in hours and a is in calories/cm2, that fits this information.

The sin bt can only take values between one and zero (definition of sin)The maximum of sin bt must be on at 1, when the maximum value of I occurs. Divide l = 610 by 1 to get a = 610.

If sin bt is equal to 1, the inverse sin will give us a value of bt = 90 degrees ( the value will be different from radians, bt = 1.57). assume the midday is the halfway point of the 12 hours of daylight, t = 90/6 = 15.
Therefore l = 610 sin 15 t where t is hours after sunrise. 
If I understand your problem correctly.

The reporter forgot to multiply the decimal by 100, making it 25%