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# Trigonometric functions

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1. The tide in a local coastal community can be modelled using a sine function. Starting at noon, the tide is at its "average" height of 3 metres measured on a pole located off of the shore. 5 hours later is high tide with the tide at a height of 5 metres measured at the same pole. 15 hours after noon is low tide with the tide at a height of 1 metre measured at the same pole. Use this information to model the tide motion using a sine function. Show all work.
2. A mass is supported by a spring so that it is at rest 0.5 m above a tabletop. The mass is pulled down 0.4 m and released at time t = 0, creating a periodic up and down motion that can be modelled using a trigonometric function. It takes 1.2 seconds to return to the lowest position each time.
a. Draw a graph showing the height of the mass above the tabletop as a function of time for the first 3 seconds of its motion.
b. Write an equation for the function in part a).
c. Use your equation to determine the height of the mass above the tabletop after
i. 0.3 seconds
ii. 0.7 seconds
iii. 2.2 seconds
d. What assumption(s) must be made for this function to be valid? Explain.