Worksheet: Hyperbolic Functions

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


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


Simplify coshsinh(𝑥)+(𝑥).

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


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

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