A boxing machine makes 60 bottles in 11 hours, how many bottles will it make in 16 hours
2 answers:
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By De Moivre's theorem,
We can stop here ...
# # #
... but we can also express these trig ratios in terms of square roots. Let and let
. Then recall that
On the left, so that
Since , we're left with
because we know to expect . Then from the Pythagorean identity, and knowing to expect
, we get
Both and
are
-periodic, so that
and
so that the answer we left in trigonometric form above is equal to