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Inverse hyperbolic functionsAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

  • What does y=\sinh^{-1}x mean?
  • Logarithmic form of \sinh^{-1}x?
  • Logarithmic form of \cosh^{-1}x?
  • Logarithmic form of \tanh^{-1}x?
  • First step in deriving a log form?
  • Why do we reject x-\sqrt{x^2+1} when finding \sinh^{-1}x?
  • Why does \cosh^{-1}x use the plus sign?
  • Why is x restricted for \tanh^{-1}x?
  • Exact value of \sinh^{-1}1?
  • Exact value of \cosh^{-1}\frac54?
  • Exact value of \tanh^{-1}\frac35?
  • How do you solve \sinh^{-1}x=k?

Exam questions on Inverse hyperbolic functions

  1. Let a=sinh⁡−1(34)a=\sinh^{-1}\left(\frac34\right) and b=tanh⁡−1(12)b=\tanh^{-1}\left(\frac12\right).
    Express a+2ba+2b as a single natural logarithm.2 marks
  2. Let c=cosh⁡−1(53)c=\cosh^{-1}\left(\frac53\right).
    Solve cosh⁡x=53\cosh x=\frac53.2 marks
  3. A student sets y=sinh⁡−1xy=\sinh^{-1}x for a real number xx, so that x=sinh⁡yx=\sinh y.
    Show that y=ln⁡(x+x2+1)y=\ln\left(x+\sqrt{x^2+1}\right).3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).