Question

3 Write a sinusoidal function in standard form that represents the temperaturo in Bellingham during the summer months. The maximum temperature of 84 degrees occurs at 4:30PM each day The minimum temperature of 41 degrees occurs at 4:30 AM each day Base your function, f(t) on time t, wheret 0 is considered to be noon, (not midnight). That is, 10:00 AM would be t -2. a) f(t) = b) Graph the function you found in part a) for one 24-hour period beginning at noon. Max Min Amplitude Period Mean Phase Shift c) At what time(s) during a 24 hour period is the temperature 70 ? d) What is the total amount of time in one period that the temperature in Bellingham is at least 70?

Answer 1

Standaral fmf huaidal funtion, 2 IT 1 whane B ouriool= 24 hr peziod 84 +41 12S 2 Mean 2. 2 A- o in 84-41 42-Ampliten de 2 2 kat 430 Pm ar 4 fresi'n at 4:30AM - phax abift all thee valuer in 2 Aubtitadiy 2 S (+4) + 2 24 2 ()= 24 125 12 24 2 -41 Tae -N

far t)-70 42 Sin 3) Sin (표(141))= +125 2 IS 4 3 + 4-3 4-3 Tㅠ-03SC33 O.3533 L1 (2 ++3 1.36108 10.63892 초 = ~0.13892 9. 13892 t--0.13892 T1:S2 AM 9.138 9 2 9:08 PM 사> 70 tor 11'S2 AM to 9:08 PM