The correct sinusoidal function with a midline at (0, -2) and a minimum point at (π/2, 37) is -39cos(x), which is not among the provided options due to a potential typo.
The student asked to write the formula of the sinusoidal function with a midline at (0, -2) and a minimum point at (π/2, 37). To identify the correct equation, we need to analyze the characteristics of sinusoidal functions. The midline is the horizontal axis around which the function oscillates, and the minimum point gives us information about the amplitude and phase shift of the function.
Given that the midline is at -2, we know that our sinusoidal function will oscillate around this value. The minimum point of the function being at (π/2, 37) indicates that the amplitude is the distance from the midline to the minimum, which is 39 (because -2 minus -39 equals 39), and that the minimum occurs at π/2, which corresponds to the cosine function starting at its maximum value and not having a phase shift. Therefore, a negative cosine function is needed to represent a minimum at π/2.
The correct answer is b) f(x) = -39cos(x). It is not listed among the options provided, indicating a possible typo in the question. Each option has the number 37, but a correct calculation of the amplitude should give us 39.