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Unformatted text preview: − π
2 = 67.5 sin π
15 t 5. (a) T (t) = 20.5 sin π t − π + 53.5
(b) Our function and the data set are graphed below. The sinusoid seems to be shifted to
the right of our data. (c) The average temperature on April 15th is approximately T (4.5) ≈ 39.00◦ F and the
average temperature on September 15th is approximately T (9.5) ≈ 73.38◦ F.
(d) Using a graphing calculator, we get the following This model predicts the average temperature for April 15th to be approximately 42.43◦ F
and the average temperature on September 15th to be approximately 70.05◦ F. This
model appears to be more accurate.
6. (a) Based on the shape of the data, we either choose A < 0 or we ﬁnd the second value of
t which closely approximates the ‘baseline’ value, F = 0.505. We choose the latter to
obtain F (t) = 0.475 sin 15 t − 2π + 0.505 = 0.475 sin 15 t + 0.505
(b) Our function and the data set are graphed below. It’s a pretty good ﬁt. 760 Applications of Trigonometry
(c) The fraction of the moon illuminated on June 1st, 2009 is approxi...
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