A robot on Mars records the temperature every Mars day

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

A robot on Mars records the temperature every Mars day. A summary series, showing every one hundredth Mars day, is shown in the table below.
Number of Mars days ( nn )01002003004005006007008009001000110012001300
Temp. ( ∘C^\circ\text{C} )-43-15-5-21-59-79-68-50-27-8-15-70-78-68
(a) Find the maximum and minimum temperatures recorded by the robot. (b) Use the data to estimate the length of a Mars year. (c) Without using technology, find a sine model for the temperature TT in terms of the number of Mars days nn. (d) Draw a scatter diagram of the data and sketch the graph of your model on the same set of axes. (e) Check your answer to c using technology. How well does your model fit?

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