Worksheet: Hyperbolic Functions

In this worksheet, we will practice defining hyperbolic functions and deriving their identities and using them to simplify expressions.

Q1:

Find an expression for sinh(2𝑥) in terms of sinh(𝑥) and cosh(𝑥).

  • A4(𝑥)(𝑥)sinhcosh
  • Bsinhcosh(𝑥)(𝑥)
  • C2(𝑥)(𝑥)sinhcosh
  • D2((𝑥)+(𝑥))sinhcosh
  • E12(𝑥)(𝑥)sinhcosh

Q2:

Simplify coshsinh(𝑥)+(𝑥).

  • A(2𝑥)cosh
  • B1
  • C0
  • Dcosh(2𝑥)1
  • Ecosh(2𝑥)

Q3:

Use the definitions of sinh and cosh to determine limsinhcosh(2𝑥)(3𝑥).

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