Task 1 In one year on the Arctic and Antarctic Circles, the amount of daylight each day varies from 0 h to 24 h. Let Ar(d) and An(d) represent the amount of daylight as a function of the day of the year d at the two locations, respectively. Describe the graph of one of the functions. Then tell how the graph of the other function relates to the first graph. BIG idea Function You can represent functions in a variety of ways (such as graphs, tables, equations, or words). Each representation is particularly useful in certain situations. Task 2 The diagram shows how cos θ, sin θ, and tan θ relate to the unit circle. Copy the diagram and show how sec θ, csc θ, and cot θ relate to the unit circle. First, find in the diagram a segment whose length is sec θ. Explain why its length is sec θ. Next, find cot θ. To do this you must add to the diagram. Use the representation of tangent as a clue for what to show for cotangent. Justify your claim for cot θ. Find csc θ in your diagram. BIG idea Function You can derive some functions from a basic parent function by a particular transformation. Functions related through these transformations are called a family of functions.