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How many solutions? (Posted on 2007-01-31) Difficulty: 4 of 5
a) Find the number of solutions of the equation sin(x)=x/573204.

b) Find the approximate difference between the two largest solutions.

No Solution Yet Submitted by Art M    
Rating: 3.7500 (4 votes)

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my thoughts | Comment 1 of 3
The solutions can be found where y=sin x and y=x/573204 intersect. Using the symmetry of the graphs, there will be an equal number of positive and negative roots. Since 573204=(2pi)(91228)+pi/2, it represents the largest solution (since any larger value of x would make sin x > 1). Also, every 2pi cycle from x=0 to x=573204 yields 2 solutions so there are 182456 positive solutions, an equal number of negative solutions, plus x=0 --> 364913 total solutions. The second largest solution is slightly less than 2pi away from 573204. I would approximate the difference between the two largest solutions as 6.283   
  Posted by Dennis on 2007-01-31 11:15:15
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