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Over a 24-hour period, the temperature in a town can be modeled by one period of a sinusoidal function. The temperature measures 70°F in the morning, rises to a high of 80°F, falls to a low of 60°F, and then rises to 70°F by the next morning.

What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?

stuck please help :/

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  1. the period is 24, so

    y = sin(π/12 x)

    The temperature varies between 60 and 80, so the center-line is y=70, and the amplitude is 10

    y = 10sin(π/12 x) + 70

    I don't know what time the temperature is 70, but if it's at 6 am, then the horizontal shift is 6 hours, meaning

    y = 10 sin(π/12 (x-6)) + 70


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