hi i tried solving this problem but i get the second part wrong? please help me. thanks you

question:
a) the maximum number of hours of sunlight is 15.3h, and occurs on June 21(day 172). The minimum number of hours of sunlight is 9.1h, and occurs on december 21(day 355). use this information. Determine the period,amplitude,phase shift, and vertical displacement.
Amplitude=max-min/2
=15.3h-(+9.1h)/2
=3.1
Period= 2pi/b
=2pi/365 (b=one cycle, number of days in a year.

Phase shift= moved to day 172 when the first day is given so this is our pahse shift. phase shift=172

vertical displacement = max+min/2
=15.3+(+9.2)/2
=12.3
t= asin2pi/b(n-b)+c
t=3.1sin2pi/365(n-172)+ 12.3
*note Pi=180

b) Determine a day when there are 14h of sunlight.
i subbed in this value with t= 14 but i got a very small number and i have a graph which does not support this. how do i correctly do this? thank you

Pi is not 180. PI should be 3.141592 in that equation.

14= 3.1sin (2PI/365 *(n-172)) + 12.3
1.7=3.1 sin(2PI/365 ((n-172))

2PI/365 (n-172)= arcsin1.7/3.1
=.580 rad

n-172=33.7
n=206

check my work.

To determine a day when there are 14 hours of sunlight, you need to solve the equation:

14 = 3.1 * sin(2π/365 * (n - 172)) + 12.3

Here's how you can solve it step by step:

1. Start with the equation: 14 = 3.1 * sin(2π/365 * (n - 172)) + 12.3.

2. Subtract 12.3 from both sides to isolate the sin term: 14 - 12.3 = 3.1 * sin(2π/365 * (n - 172)).

3. Simplify on the left side: 1.7 = 3.1 * sin(2π/365 * (n - 172)).

4. Divide both sides by 3.1 to isolate the sin term: 1.7/3.1 = sin(2π/365 * (n - 172)).

5. Use the inverse sine function (sin^-1) to find the angle: sin^-1(1.7/3.1) = 2π/365 * (n - 172).

6. Calculate the angle using a calculator: sin^-1(1.7/3.1) ≈ 32.635 degrees.

7. Convert the angle to radians by multiplying it by π/180: 32.635 * (π/180) ≈ 0.569.

8. Substitute the angle back into the equation: 0.569 = 2π/365 * (n - 172).

9. Multiply both sides by 365/(2π) to solve for n - 172: n - 172 = 0.569 * (365/(2π)).

10. Add 172 to both sides to solve for n: n = 0.569 * (365/(2π)) + 172.

11. Calculate the value of n using a calculator: n ≈ 202.268.

12. Since n represents the day number, round it to the nearest whole number: n ≈ 202.

Therefore, the day when there are approximately 14 hours of sunlight is day 202.