anonymous
  • anonymous
Can someone help me finish this problem I took it as far as I could... If x=9sinθ, use trigonometric substitution to write √(81-x^2) as a trigonometric function of θ, where -pi/2<θ
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
So far I have √(81-9sinθ^2) 81√(1-sinθ^2) 1-sin^2θ=1/cscθ ?
anonymous
  • anonymous
or maybe It is 9√(1-sinθ^2)...
anonymous
  • anonymous
yes

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anonymous
  • anonymous
your second post was right
anonymous
  • anonymous
√(81-81sinθ^2) <--- (9sinθ)^2 = 81sinθ^2 = 9√(1-sinθ^2)
anonymous
  • anonymous
next you need to figure out which trig substitution to use
anonymous
  • anonymous
Thank you! would the answer be 9cscθ then?
anonymous
  • anonymous
\[\sin ^{2}\theta+\cos ^{2}\theta = 1\] is a where you want to start thinking about your substitution
anonymous
  • anonymous
the answer isn't 9cscθ, but you are almost there
anonymous
  • anonymous
use \[1-\sin ^{2}\theta = \cos ^{2}\theta\]
anonymous
  • anonymous
oh ok...where did the cos come from? I thought sinθ=1/cscθ so in this case it would be 1-sin^2θ=1/cscθ ?
anonymous
  • anonymous
ok so 9cosθ?
anonymous
  • anonymous
yes :)
anonymous
  • anonymous
Sweet! thanks a bunch!

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