Unformatted text preview: mately F (1) ≈ 0.60
(d) Using a graphing calculator, we get the following. This model predicts that the fraction of the moon illuminated on June 1st, 2009 is
approximately 0.59. This appears to be a better ﬁt to the data than our ﬁrst model.
7. (a) k = 5 lbs. and m =
16 slugs (b) x(t) = sin 4t + . The object ﬁrst passes through the equilibrium point when t =
0.39 seconds after the motion starts. At this time, the object is heading upwards.
8 ≈ π
(c) x(t) = 22 sin 4t + 74 . The object passes through the equilibrium point heading downwards for the third time when t = 17π ≈ 3.34 seconds.
16 11.2 The Law of Sines 11.2 761 The Law of Sines Trigonometry literally means ‘measuring triangles’ and with Chapter 10 under our belts, we are
more than prepared to do just that. The main goal of this section and the next is to develop
theorems which allow us to ‘solve’ triangles – that is, ﬁnd the length of each side of a triangle
and the measure of each of its angles. In Sections 10.2, 10.3 and 1...
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