anonymous
  • anonymous
How can I show that the function y=(cos^-1)x satisfies the equation [(d^2y)/(dx^2)]=-cot y cosec^2 y?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1443184414753:dw| I tried subbing y into the equation, is that what I'm meant to do?
IrishBoy123
  • IrishBoy123
yes you did \(\cos y = x\) implicitly?
anonymous
  • anonymous
@IrishBoy123 You mean like this: |dw:1443185241885:dw|

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IrishBoy123
  • IrishBoy123
well, no, i was thinking doing it this way: \( \cos y = x\) \(-sin y \, y' = 1\) \(- \cos y \, (y')^2 - \sin y \, y' \, y '' = 0\) then rearranging all of that.
anonymous
  • anonymous
Oh that makes sense, thank you so much! :)
IrishBoy123
  • IrishBoy123
typo in last line \(- \cos y \, (y')^2 - \sin y \, y '' = 0\)

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