You are sitting on a pier when you notice a bottle bobbing in the waves. The bottle
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Question:
a) Sketch and label a graph of the bottle's distance below the pier for 15 s. Assume that at t = 0, the bottle is closest to the bottom of the pier.
b) Determine the period and the amplitude of the function.
c) Which function would you consider to be a better model of the situation, sine or cosine? Explain.
d) Write the equation of the sine function that models the bottle's distance below the pier.
e) You can reach 0.9 m below the pier. Use your equation to estimate the length of time, to the nearest tenth of a second, that the bottle is within your reach during one cycle.
f) Write the cosine function for this situation. Would your answer for part
g) change using this equation? Explain. B2. Two sinusoidal functions are shown in the graph. YA 12 7
h) Which characteristics of the two graphs are the same?
i) Which parameters must change to transform the graph of f(x) to the graph of g(x)?
j) Determine the equation for each of the graphs in the 4 - form y = a cos b(x - c) + d. 0
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