Hyperbolic Functions Calculator

Hyperbolic Functions Calculator

Calculate sinh, cosh, tanh, sech, csch, and coth.

Last updated: June 2026 | By Patchworkr Team

Input Value

sinh(x)
1.175
cosh(x)
1.543
tanh(x)
0.762
sech(x)
0.648
csch(x)
0.851
coth(x)
1.313

What these are

Hyperbolic functions are the exponential analogs of circular trig functions.

Key identity

cosh^2(x) - sinh^2(x) = 1.

Worked Example

Verify the identity at x = 1.

1. sinh(1) ≈ 1.1752

2. cosh(1) ≈ 1.5431

3. cosh^2(1) - sinh^2(1) ≈ 1

Final answer: identity verified

Frequently Asked Questions

Are these periodic?

No. They grow exponentially rather than repeating.

What happens at x = 0?

sinh(0) = 0, cosh(0) = 1, tanh(0) = 0.

Why is cosh always >= 1?

Because it is the average of two positive exponentials.

What is csch at zero?

It is undefined, so the calculator shows infinity.

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