triginometry

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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

  • triginometry -

    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.

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