A spider rests on the blade of a ceiling fan, as shown in the figures. A stopwatch is started, at which point the time is t= 0 seconds. When t=0, the spider is at its maximum distance from the wall, 2.5 m away from the wall (Figure 1). The spider first reaches its minimum distance from the wall, 1.5 m away from the wall, when t = 1 second (Figure 2). When t=2 seconds, the spider is back to its maximum distance from the wall. The spider continues to move in a circle, so that the spider's distance from the wall over time can be modeled by a sinusoidal function. Let f(t) be the distance between the spider and the wall 1 seconds after starting the stopwatch. (a) Graph the function y=f (t) that models the distance between the spider and the wall. • First choose the appropriate starting graph from the ones below. • Then transform it to make a graph that shows the distance between the spider and the wall from the stopwatch data. 2.5 m * * Figure 1: = 0 1,5 m Figure 2: = 1

The height of a person on a Ferris wheel is given by the function h(t)=42 cos(2t). Q: How long does it take to make two complete cycles on the Ferris wheel? Assume there are no stops. Round your answer to a whole number. Ans: It takes seconds to make two cycles. Your Answer: Answer

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