cosh and sinh calculator

What are sinh and cosh?

The functions sinh (hyperbolic sine) and cosh (hyperbolic cosine) are core mathematical functions used in algebra, calculus, differential equations, and physics. They are defined using exponentials:

• sinh(x) = (e^x - e^-x) / 2
• cosh(x) = (e^x + e^-x) / 2

Even though these formulas look similar to regular sine and cosine, hyperbolic functions describe hyperbolas rather than circles.

How to use this cosh and sinh calculator

Step-by-step

• Enter your x value in the input box.
• Select whether your input is in radians or degrees.
• Choose how many decimal places you want.
• Click Calculate to view sinh(x), cosh(x), tanh(x), and the identity check.

This tool computes everything instantly and is useful for homework checks, quick engineering estimates, and self-study.

Important identities

One of the most useful hyperbolic identities is:

cosh²(x) - sinh²(x) = 1

This identity is the hyperbolic counterpart to the trigonometric relation cos²(x) + sin²(x) = 1. In the calculator output, the identity is checked numerically so you can verify your result quality.

Example values

At x = 0

• sinh(0) = 0
• cosh(0) = 1

At x = 1 (radian)

• sinh(1) ≈ 1.1752
• cosh(1) ≈ 1.5431

At x = 2 (radians)

• sinh(2) ≈ 3.6269
• cosh(2) ≈ 3.7622

Where hyperbolic functions are used

• Physics: relativistic motion, wave equations, and potential problems.
• Engineering: catenary curves in suspended cables and bridge modeling.
• Mathematics: solving linear differential equations and complex analysis.
• Computer graphics: geometric transformations and shape modeling.

Common mistakes to avoid

• Confusing sinh/cosh with sin/cos (they are different functions).
• Mixing degrees and radians unintentionally.
• Rounding too early in multi-step problems.
• Using very large x values that can cause overflow in exponential calculations.

Quick FAQ

Is cosh(x) ever negative?

No. For real x, cosh(x) is always greater than or equal to 1.

Can sinh(x) be negative?

Yes. sinh(x) is an odd function, so negative x values produce negative results.

What is tanh(x)?

tanh(x) = sinh(x) / cosh(x). This calculator also shows tanh(x) for convenience.

Final note

If you regularly work with hyperbolic functions, bookmarking a reliable calculator can save time and reduce algebra mistakes. Use this page to get fast values, check identities, and build confidence while solving equations involving sinh and cosh.