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Question: Solutions to sin(x)=sin(1/x)

Question:Solutions to sin(x)=sin(1/x)

Thomas Madden 183
August 08 2005
1
When I graph the functions sin(x) and sin(1/x) in maple I can see that these functions will intercept each other an infinite number of times. However, when I write the equation sin(x)=sin(1/x) and click on it and choose solve maple only ruturns the obvious solutions 1 and -1. I can see that sin(1/x) ->0 as x increases (x>2/Pi) and that sin(x) will repeatedly assume all values between 0 and 1 as x increases. In general, how can you find the values where the two functions intercept on some interval where x>1, say [2,10], and also on some interval where x is between 0 and 1? Can I do this with Maple both algebraically and numerically? Thank you in advance for any response.
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