perplexus.info :: Just Math : Sparse Sine Settlement

Sparse Sine Settlement (Posted on 2014-09-03)

Find the minimum positive integer N such that:

(sin 45^o)^-1*(sin 46^o)^-1+ (sin 47^o)^-1*(sin 48^o)^-1+.....+ (sin 133^o)^-1*(sin 134^o)^-1
= (sin N^o)^-1

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer-aided solution

| Comment 1 of 2

5 point 10

10 Dr=#pi/180

20 for I=45 to 133 step 2

30 T=T+1/(sin(I*Dr)*sin((I+1)*Dr))

40 next

50 Rcp=1/T

60 N=atan(Rcp/sqrt(1-Rcp*Rcp))/Dr

70 print N

does calculations to 48 positions after the decimal point and finds the answer is 1.0 degrees.

Posted by Charlie on 2014-09-03 18:03:11

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