minatsukisaya95
  • minatsukisaya95
x=a(b-sinb),y=a(1-cos b), prove dy/dx=cot(b/2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
dy/db = asinb dx/db = a(1-cosb) helps ?
anonymous
  • anonymous
another hint : now you can divide dy/db by dx/db and get dy/dx !
anonymous
  • anonymous
ill help more: ( dy/db ) / (dx/db) = asinb/ a(1-cosb) = sinb / (1-cosb) = dy/dx

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anonymous
  • anonymous
now it is just trigo.
anonymous
  • anonymous
if you dont like the idea of dividing dy/db by dx/db you can as well use the chain rule : dy/dx = dy/db * db/dx and you can find db/dx by isolating b from the equation with x and finding db/dx.
minatsukisaya95
  • minatsukisaya95
the answer i got is different from what to prove
anonymous
  • anonymous
you get dy/dx = sinb / (1-cosb)
anonymous
  • anonymous
now it can be shown that it is the same as cot(b/2)
anonymous
  • anonymous
hint : sin(b) = sin(2 * b/2) cos(b) = cos(2*b/2) use the formulas for double angle now.
minatsukisaya95
  • minatsukisaya95
yes i get that but how do we solve that to get cot(b/2)
anonymous
  • anonymous
look at my last response it should help you
anonymous
  • anonymous
sin(b) = 2sin(b/2)cos(b/2) cos(b) = cos^2(b/2) - sin^2(b/2) so sinb / (1-cosb) = 2sin(b/2)cos(b/2) / (1- cos^2(b/2) + sin^2(b/2))
anonymous
  • anonymous
i hope you can do it from here.
anonymous
  • anonymous
@minatsukisaya95 are you there ?
minatsukisaya95
  • minatsukisaya95
yes thank u i got it
anonymous
  • anonymous
yw

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