anonymous
  • anonymous
How can I simplify.... tan(arcsin x) ??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
tan= sin/cos
anonymous
  • anonymous
Yep, so does it become... \[\frac{ \sin(\sin^{-1} x) }{ \cos(\sin^{-1} x) }\] ??
anonymous
  • anonymous
and then \[\frac{ x }{ \cos (\sin^{-1}x) }\]

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anonymous
  • anonymous
yes
anonymous
  • anonymous
Is that the furthest I can simplify?
anonymous
  • anonymous
i think no
anonymous
  • anonymous
Do have any hints on what I can do?
geerky42
  • geerky42
Drawing triangle would be helpful.
geerky42
  • geerky42
Let there be a triangle with opposite side of \(x\), and hypotenuse of \(1\). By Pythagorean Theorem, adjacent side would be \(\sqrt{1-x^2}\). |dw:1433108189889:dw| From here, we can see that \(\sin\theta = \dfrac{x}{1} = x\), hence \(\theta = \arcsin(x)\) Now, what is \(\tan\theta = \tan(\arcsin(x))\)?
geerky42
  • geerky42
Remember SOH CAH TOA?
anonymous
  • anonymous
Ohh so tan is opposite/adjacent .... so \[\frac{ x }{ \sqrt{1-x^2} }\]
geerky42
  • geerky42
Gotcha
anonymous
  • anonymous
Awesomeness!! XD
anonymous
  • anonymous
Thanks so much @geerky42
geerky42
  • geerky42
Welcome!

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