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  • 项目:分析三角测量

    The sine and cosine functions can be used to model fluctuations in temperature data throughout the year. For example, the average monthly temperatures for a city  were used to create the following graph:

    lesson content

    A trigonometric function that provides a good fit to model this data is  T ( m ) = 26.74 sin ⁡ ( 0.48 m − 2.03 ) + 45.6.
    ::T(m)=26.74sin(0.48m-2.03)+45.6。

    Project: Create a Model of the Temperature Data to Plan a  F amily Vacation
    ::项目:建立温度数据模型,以规划家庭假期

    Four members of a family are using a democratic approach to choose a vacation. Each family member wants to visit a different city. Your task is to create a model of the average monthly temperatures for all four cities on one graph,  so the family can use this information to discuss the ideal location and time of year. The four cities chosen are  Bar Harbor, Maine; Maui, Hawaii; Anchorage, Alaska; and Orlando, Florida.
    ::每个家庭成员都想访问不同的城市。你的任务是在一张图表上为所有四个城市创建一个月平均气温模型,以便家庭能够利用这些信息讨论年度的理想地点和时间。 所选择的四个城市是缅因州巴港、夏威夷毛伊、阿拉斯加州安克雷奇和佛罗里达州奥兰多。

    S ource:  
    ::资料来源:

    1. Graph the data.
      ::绘制数据图。
    2. Write a trigonometric equation for each city using the sine function that best models this situation.
      ::为每个城市写三角方程 使用正弦函数 来模拟这种情况
    3. Rewrite the equation using the cosine function using a cofunction identity.
      ::使用余弦函数重写方程式, 使用共用元件身份重写此方程式 。
    4. Graph the function that approximates the data.
      ::图形显示与数据相近的函数。
    5. What features of the data are represented by a , b , h , and k  in your equation? Explain the meaning of these values in context.
      ::您的方程中以 a、 b、 h 和 k 表示的数据有哪些特征? 请解释这些值在上下文中的含义 。
    6. Set up an equation to solve for the times that the average monthly temperature reached a specific value within the range of the dataset.
      ::设置一个方程式, 以解析平均月温度在数据集范围内达到特定值的时间 。
    7. Solve the equation. On how many dates in the domain of the dataset was this temperature reached? 
      ::解析方程。 在数据集域中, 到达多少日期的温度 ?