Laplace Transform of cosh(at)
The Laplace transform of cosh(at) is s/(s² − a²). See the table rule behind it, then edit the function to transform anything else.
L{cosh(at)} = s/(s² − a²). L{cosh(at)} = s/(s² − a²).
Use t as the variable. Examples: t^3, e^(-2t), sin(3t), t*cos(2t), 4t^2+3. Write δ(t) as delta(t).
The result
L{cosh(at)} = s/(s² − a²)
Worked example with numbers: L{cosh(2t)} = s/(s^2 - 4)
- L{cosh(2t)} = s/(s^2 - 4) Table rule: L{e^(at)cosh(bt)} = (s − a)/((s − a)² - b²)
L{cosh(at)} = s/(s² − a²).
More hyperbolic transforms
Other transforms
Frequently asked questions
What is the Laplace transform of cosh(at)? ▾
L{cosh(at)} = s/(s² − a²). L{cosh(at)} = s/(s² − a²).
Which rule gives the transform of cosh(at)? ▾
L{e^(at)cosh(bt)} = (s − a)/((s − a)² - b²) applied to cosh(2t).
How do I get back from F(s) to f(t)? ▾
Use the inverse Laplace transform. Split F(s) into partial fractions and invert each piece with the same table read backwards — the inverse Laplace transform calculator does this step by step.
About this Calculator
The Laplace transform of cosh(at) is s/(s² − a²). See the table rule behind it, then edit the function to transform anything else.