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 s i n h ( 2 𝑥 ) in terms of s i n h ( 𝑥 ) and c o s h ( 𝑥 ) .

  • A 2 ( 𝑥 ) ( 𝑥 ) s i n h c o s h
  • B 4 ( 𝑥 ) ( 𝑥 ) s i n h c o s h
  • C 2 ( ( 𝑥 ) + ( 𝑥 ) ) s i n h c o s h
  • D 1 2 ( 𝑥 ) ( 𝑥 ) s i n h c o s h
  • E s i n h c o s h ( 𝑥 ) ( 𝑥 )

Q2:

Simplify c o s h s i n h ( 𝑥 ) + ( 𝑥 ) .

  • A ( 2 𝑥 ) c o s h
  • B0
  • C c o s h ( 2 𝑥 ) 1
  • D c o s h ( 2 𝑥 )
  • E1

Q3:

Use the definitions of s i n h and c o s h to determine l i m s i n h c o s h ( 2 𝑥 ) ( 3 𝑥 ) .

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