Can someone please explain this to me?? I'm really stuck on it. First of all, i don't know if I should use cosine or sine for the function because it only says to make a sinusoidal function that models the data, and a sinusoidal function could be either sine or cosine. PLEASE HELP!!!

Trigonometric Stuff: It is possible to use a sinusoidal function to model the amount of perceived daylight in a certain location over the course of a year. For Portland, Oregon, there is a minimum of 9 hours of “daylight” on the 1st day of winter and a maximum of 17 hours of “daylight” on the 1st day of summer. Let D represent the number of hours of “daylight” in Portland, Oregon, T days after the 1st day of spring (assume that T = 0 corresponds to March 20th). You may assume that 1 year has 365 days.

Find a formula for such a function, being sure to explain the practical meanings of any important pieces of the formula (amplitude,midline, and period). Use your formula to determine on what days of the year (month and day, not just T’s value) Portland has about 11hours of “daylight” and about 15 hours of “daylight”. Please round to the nearest day, if not exact.

asked by Geni
  1. Please can someone help!?!!?

    posted by Geni
  2. well, you could say
    D = .5(9+17)+ A sin wt + B cos wt
    that is the midline , 13
    if you start at the minimum with t = 0
    and D = 9
    then to get a minimum at t = 0
    say D = 13 + A sin 0 + B cos 0
    D = 13 + 0 + B
    but we know D = 9
    so B = -4
    so we have
    D = 13 - 4 cos w t
    now when t = 365
    w t = 2 pi, a whole circle
    w * 365 = 2 pi
    w = 2 pi/365
    d = 13 - 4 cos (2 pi t/365)

    posted by Damon
  3. sine function

    it starts at the median (average) day length and increases to the summer solstice, then decreases to the winter solstice, then increases back to the average at the vernal equinox

    the midline is the average ... (9 + 17) / 2

    the amplitude is max minus average

    the period is 365 (days)

    posted by Scott
  4. whoops I took t = 0 at Jan 1
    should be at March 20 or 1/4 year after Jan 1
    alter that to get min at 1/4 year
    D = 13 - 4 cos (2pi t/365 - x)
    when t = (1/4)(365) or 91.25 days
    2 pi * .25 - x = 0
    x = 2 pi * .25
    so in the end
    D = 13 - 4 cos (2 pi t/365 - pi/2)

    posted by Damon
  5. which is
    D = 13 + 4 sin (2 pi t/365)

    posted by Damon
  6. Thank you so much!!! It makes more sense now!!! Thanks again!!

    posted by Geni

Respond to this Question

First Name

Your Response

Similar Questions

  1. Graphing trigonometric function

    sine and cosine have a period 2pi tangent and cotangent have period pi Can someone explain why? thanks a lot. well tangent is sine/cosine and there a place where the tangent function is undefined and that is where the asymptotes
  2. calculus

    the equation y+y"=0 is the differential equation of? a.)sine function b.)sinusoidal c.)cosine function d.) a and c e.) abc
  3. pre calc

    The Identity Function The Squaring Function The Cubing Function The Reciprocal Function The Square Root Function The Exponential Functional Lo The Natural Logarithum Function The Sine Function The Cosine Function The Absolute
  4. Math

    3. At the end of a dock, high tide of 14 m is recorded at 9:00 a.m. Low tide of 6 m is recorded at 3:00 p.m. A sinusoidal function can model the water depth versus time. a) Construct a model for the water depth using a cosine
  5. Algebra 2

    Over a 24-hour period, the temperature in a town can be modeled by one period of a sinusoidal function. The temperature measures 70°F in the morning, rises to a high of 80°F, falls to a low of 60°F, and then rises to 70°F by
  6. trigonometry

    An object is attached by a string to the end of a spring. When the weight is released it starts oscillating vertically in a periodic way that can be modeled by a trigonometric function. The object's average height is −20 cm
  7. Calculus AB

    If a sinusoidal function has a local maximum at (3,8) and the next local minimum at (7,-2), 1) What is the equation of a cosine function that has a graph characterized in the statement above 2) What is the equation of a sine
  8. trig

    1. Write a sinusoidal function for the function with a period of 6. The function has a max of 3 at x=2 and a low point of -1. 2. Write a sinusoidal function for the function with a period of 5. The function has a max of 7 at x=1.
  9. Pre-Cal: Word Problem

    I'm having a lot of trouble on this word problem. Can someone help me plz? To define the inverse sine function, we restrict the domain of sine to the interval ______. On this interval the sine function is one-to-one, and its
  10. Trigonometry

    Evaluate the sine, cosine and tangent of -7pi/3. I got 1/2, sq. root of 3/2 and sq. root of three. My book says the sine and the tangent are negative, but I don't know why? Can you explain the rule??

More Similar Questions