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IB MAI HL Geometry & Trigonometry Topic 3.4 Trigonometric Functions (id: c4fe6b6

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admin 发表于 2024-2-16 23:12:33 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Geometry & Trigonometry Topic 3.4 Trigonometric Functions,类别为 IB数学

[填空题]
The temperature in N9:.fk yl+t 5svr.s kykew York r9/+m;gw140sao pmd sutlh gq3anges from $-4^{\circ}C$ to $22^{\circ}C$ throughout the course of a year. The temperature, T, can be modelled by the function
T(t)=−acos(bt)+d,
Where t is time measured in months from the beginning of the year, and a, b and d∈Z+.
1.Show that
(1)a=13;   
(2)b=30;   
(3)d=9.   
2.Sketch the function 0≤t≤12, clearly labelling the coordinates of the maximum and minimum points.
3.Find the temperature when t=4.
4.(1)Determine the number of months in a year that the temperature is above $^{\circ}C$.
(2)Find the probability that on a randomly chosen day of the year, the temperature is above $9^{\circ}C$.
5.If the temperature in New York ranged from $-7^{\circ}C$to $25^{\circ}C$ instead of $-4^{\circ}C$ to $22^{\circ}C$, describe how this would affect the probability found in (d) part (ii).




参考答案:
空格1: 13±2%空格2: 30±2%空格3: 9±2%


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