Question

1. you (safely) bungee jump from a 200-feet tall bridge in your town. your distance above the water’s surface depends on the time since you jumped. sketch a reasonable graph. (3 points)

for questions 2 - 5, sketch the graph of each function, showing two complete cycles between (-2pi,2pi). label the x-coordinates of any zeros or asymptotes. (3 points each)

1. ( y = cos x )

na

1. ( y = \tan x )

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1. ( y = sin x )

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1. ( y = csc x )

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Explanation:

Answer:

1. A graph starting at (0, 200), decreasing to a minimum distance above water, oscillating with decreasing amplitude until stabilizing at a constant distance.
2. Cosine wave with zeros at $-\frac{3\pi}{2}, -\frac{\pi}{2}, \frac{\pi}{2}, \frac{3\pi}{2}$, peaks at $(-2\pi,1), (0,1), (2\pi,1)$, troughs at $(-\pi,-1), (\pi,-1)$ over $[-2\pi,2\pi]$.
3. Tangent graph with asymptotes at $x=-\frac{3\pi}{2}, -\frac{\pi}{2}, \frac{\pi}{2}, \frac{3\pi}{2}$, zeros at $x=-2\pi, -\pi, 0, \pi, 2\pi$ over $[-2\pi,2\pi]$.
4. Sine wave with zeros at $-2\pi, -\pi, 0, \pi, 2\pi$, peaks at $(-\frac{3\pi}{2},1), (\frac{\pi}{2},1)$, troughs at $(-\frac{\pi}{2},-1), (\frac{3\pi}{2},-1)$ over $[-2\pi,2\pi]$.
5. Cosecant graph with asymptotes at $x=-2\pi, -\pi, 0, \pi, 2\pi$, vertices at $(-\frac{3\pi}{2},1), (-\frac{\pi}{2},-1), (\frac{\pi}{2},1), (\frac{3\pi}{2},-1)$ over $[-2\pi,2\pi]$.