Traditional Culture Encyclopedia - The 24 Solar Terms - As shown in the figure, during the Spring Festival, the temperature in a certain place changes periodically day and night, and the change of temperature y with time x approximately satisfies the funct
As shown in the figure, during the Spring Festival, the temperature in a certain place changes periodically day and night, and the change of temperature y with time x approximately satisfies the funct
As shown in the figure, during the Spring Festival, the temperature in a certain place changes periodically day and night, and the change of temperature y with time x approximately satisfies the function y=Asin(ωx+φ)+b, (A>0, ω > 0,
According to the daily minimum temperature of -3℃ at 2 am and the maximum temperature of 9℃ at 14 pm.
Given that t is 2* 12=24, ω=π/ 12.
The maximum value of Asin(ωx+φ)+b is sin(ωx+φ) 1, and the minimum value is-1.
So A+b=9 -A+b=-3, A=6, b = 3;;
By 6sin(π / 12 ×2+? )+3=-3
And-π
So y=6sin(π/12 x-2π /3 )+3.
(2)Sin(π/ 12x-2π/3)+3 = 0 =- 12( 10),
So π/12 x-2π/ 3 =2kπ-π /6 or π/12 x-2π /3 =2kπ+7π /6, k∈Z( 12 point),
From 0 ≤ x < 24, x=6 or x=22, that is, the temperature at 6 o'clock or 22 o'clock every day is 0℃( 14 minutes).
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