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For Exercises 61-62, describe the differences in the graphs of
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- Meteorology The normal monthly high temperatures H (in degrees Fahrenheit) in Erie, Pennsylvania, are approximated by Ht=57.5418.53cost614.03sint6 and the normal monthly low temperatures L are approximated by Lt=42.0315.99cost614.32sint6 where t is the time (in months), with t=1 corresponding to January (see figure). (a) What is the period of each function ? (b) During what part of the year is the difference between the normal high and normal low temperatures greatest ? When is it least ? (c) The sun is northernmost in the sky around June 21, but the graph shows the warmest temperatures at a later date. Approximate the lag time of the temperatures relative to the position of the sun.arrow_forwardThe number of hours (h) of sunlight per day in Prescott, Arizona, can be modeled by h = 2.325sin π/6 (t-2.667) + 12.155 where t is measured in months and t = 0 represents January 1. On which days of the year are there 10 hours of sunlight in Prescott?arrow_forward1. To obtain the graph of y=asinb(x-h)+k, explain what each of the values of a, b, h, and k affects the graph of function y=sinx.arrow_forward
- Answer this question.arrow_forwardGraph the function y =-2 cos(2x - p)arrow_forwardA child builds two wooden train sets. The path of one of the trains can be represented by the function y = 2cos²x, where y represents the distance of the train from the child as a function of x minutes. The distance from the child to the second train can be represented by the function y = 3 + cos x. What is the number of minutes it will take until the two trains are first equidistant from the child? a b C d 6 minutes n minutes 1 minute 1.5 minutesarrow_forward
- b.) Interpret your answer to part (a) in contextarrow_forwardCompare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following choices is the correct comparison? a The cosine function has a phase shift that is 12 that of the sine function and in the same direction; the amplitude of the cosine function is 2 times that of the sine function. b The cosine function has a phase shift that is 12 that of the sine function and in the opposite direction; the amplitude of the cosine function is 12 that of the sine function. c The cosine function has a phase shift that is 2 times larger than the phase shift of the sine function and in the same direction; the amplitude of the cosine function is 12 that of the sine function. d The cosine function has a phase shift that is 2 times larger than that of the sine function and in the opposite direction; the amplitude of the cosine function is 2 times that of the sine function.arrow_forwardGiven y=-3sin[2(x-60)]+1, what is the period of the function?arrow_forward
- a. Solve 2 cos(2x) = √2 for xarrow_forward.arrow_forwardIn desert areas of the western United States, lizards and other reptiles are harvested for sale as pets. Because reptiles hibernate during the winter months, no reptiles are gathered during the months of January, February, November, and December. The number of lizards harvested during the remaining months can be modeled as h(m) = 15.3 sin(0.805m + 2.95) + 16.7 where m is the month of the year (i.e., m = 3 represents March), 3 sm s 10.+ (a) Calculate the amplitude and average value of the model. (Round your answer to one decimal place.) amplitude lizards average value | lizards (b) Calculate the highest and lowest monthly harvests. Write a sentence interpreting these numbers in context. (Round your answer to the nearest integer.) The most lizards harvested in one month is lizard(s) and the least harvested in one month (during harvest season) is lizard(s). (c) Calculate the period of the model. (Round your answer to three decimal places.) Is this model useful for m outside the stated…arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning