Further MathsYears 12–13Hyperbolic Functions
Hyperbolic functions and identities
Define sinh, cosh, tanh and their inverses; prove and use hyperbolic identities; differentiate and integrate
What you'll learn
- 1
Imagine a hanging chain — like a washing line between two poles. Its shape is called a 'catenary'.
- 2
What everyday object hangs in a catenary shape?
- 3
Drag the slider to see how cosh(x) changes — it's like a smooth U-shape.
- 4
Let's calculate cosh(0) using its definition: cosh(x) = (eˣ + e⁻ˣ)/2.
- 5
What is sinh(0) if sinh(x) = (eˣ − e⁻ˣ)/2?
- 6
A key identity is cosh²(x) − sinh²(x) = 1 — like a circle identity but with a minus!
- 7
What does cosh²(x) − sinh²(x) always equal?
Practise Hyperbolic functions and identities with Whizlo
Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.