Apply the procedure to
sin2 (a)
an+1 = 4sin2 (a)(1 - sin2 (a))
= 4sin2 (a)cos2 (a)
= (2sin(a)cos(a))^2
= (sin(2a))^2
= sin2 (2a)
Each term just doubles the angle from the last.
Now, in the interval [0,2π) we know
sin2 (1π/45) = sin2 (44π/45) = sin2 (46π/45) = sin2 (89π/45)
So the question becomes how many times do we double the original angle to get one of these?
Here's a table of n, multiple of π/45 mod 90
0 1
1 2
2 4
3 8
4 16
5 32
6 64
7 38
8 76
9 62
10 34
11 68
12 46 <---- we have a hit. The answer is 12.
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Posted by Jer
on 2019-01-08 11:36:32 |
Full solution
