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Import favorites MVNU Students Ho... A ALEKS - Jameson C... Trigonometric Graphs Word problem involving a sine or cosine function: Problem type 2 1//5 Jameson Español For a given location, the daily number of sunlight hours fluctuates throughout the year. Suppose that the number of sunlight hours is given by the following function. D(t)=12-6.6 cos((2pi)/(365)t) In this equation, D(t) is the number of hours of sunlight in a day, and t is the number of days after June 21^("st "). Find the following. If necessary, round to the nearest hundredth. Maximum number of hours of sunlight in a day: ◻ Period of D : ◻ days Amplitude of D : ◻ hours of sunlight in a day Explanation Check Task View (C) 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Accessibility Type here to search

Import favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Graphs\newlineWord problem involving a sine or cosine function: Problem type 22\newline1/5 1 / 5 \newlineJameson\newlineEspañol\newlineFor a given location, the daily number of sunlight hours fluctuates throughout the year. Suppose that the number of sunlight hours is given by the following function.\newlineD(t)=12−6.6cos⁡(2π365t) D(t)=12-6.6 \cos \left(\frac{2 \pi}{365} t\right) \newlineIn this equation, D(t) D(t) is the number of hours of sunlight in a day, and t t is the number of days after June 21st  21^{\text {st }} .\newlineFind the following. If necessary, round to the nearest hundredth.\newlineMaximum number of hours of sunlight in a day: □ \square \newlinePeriod of D D : □ \square days\newlineAmplitude of D D : □ \square hours of sunlight in a day\newlineExplanation\newlineCheck\newlineTask View\newline(C) 20242024 McGraw Hill LLC. All Rights Reserved. Terms of Use\newlinePrivacy Center\newlineAccessibility\newlineType here to search

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Q. Import favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Graphs\newlineWord problem involving a sine or cosine function: Problem type 22\newline1/5 1 / 5 \newlineJameson\newlineEspañol\newlineFor a given location, the daily number of sunlight hours fluctuates throughout the year. Suppose that the number of sunlight hours is given by the following function.\newlineD(t)=12−6.6cos⁡(2π365t) D(t)=12-6.6 \cos \left(\frac{2 \pi}{365} t\right) \newlineIn this equation, D(t) D(t) is the number of hours of sunlight in a day, and t t is the number of days after June 21st  21^{\text {st }} .\newlineFind the following. If necessary, round to the nearest hundredth.\newlineMaximum number of hours of sunlight in a day: □ \square \newlinePeriod of D D : □ \square days\newlineAmplitude of D D : □ \square hours of sunlight in a day\newlineExplanation\newlineCheck\newlineTask View\newline(C) 20242024 McGraw Hill LLC. All Rights Reserved. Terms of Use\newlinePrivacy Center\newlineAccessibility\newlineType here to search
  1. Identify Maximum Sunlight Hours: To find the maximum number of sunlight hours, look at the constant and the amplitude in the function D(t)=12−6.6cos⁡(2π365t)D(t)=12-6.6 \cos\left(\frac{2\pi}{365}t\right). The max sunlight hours will be when the cosine function is at its minimum, which is −1-1.
  2. Calculate Maximum Sunlight Hours: Calculate the maximum number of sunlight hours: Dmax=12−6.6×(−1)=12+6.6=18.6D_{\text{max}} = 12 - 6.6 \times (-1) = 12 + 6.6 = 18.6 hours.
  3. Determine Period of Function: The period of the function D(t)D(t) is the time it takes for the function to repeat. Since the cosine function has a period of 2π2\pi, and there's a coefficient of (2π/365)(2\pi/365) in front of tt, the period of D(t)D(t) is 365365 days.
  4. Find Amplitude of Function: The amplitude of the function D(t)D(t) is the absolute value of the coefficient in front of the cosine function, which is 6.66.6 hours of sunlight in a day.

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