cosh()

The PHP cosh() function returns the hyperbolic cosine of a number. Unlike the ordinary cos() function, which describes points on a circle, the hyperbolic cosine describes points on a hyperbola and shows up in physics (the shape of a hanging cable, a "catenary"), engineering, and numerical math. This page explains what cosh() computes, its syntax and return value, and the gotchas to watch for.

Syntax

cosh(float $num): float

• $num — the value to process, interpreted in radians (not degrees).
• Return value — a float: the hyperbolic cosine of $num.

Mathematically, the function evaluates:

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

Because both e^x and e^-x are always positive, cosh(x) is always ≥ 1. Its minimum value, 1, occurs at x = 0, and it grows quickly for large positive or negative inputs. The function is even, meaning cosh(-x) === cosh(x).

Basic Example

We store the input in a variable, pass it to cosh(), and print the result. PHP returns roughly 3.7621956910836 for an input of 2.

A Range of Values

The example below shows how cosh() behaves across several inputs, including the special case at 0 and the symmetry between positive and negative arguments:

<?php
echo cosh(0);   // 1 — the minimum value
echo "\n";
echo cosh(1);   // 1.5430806348152
echo "\n";
echo cosh(-1);  // 1.5430806348152 — same as cosh(1), the function is even
echo "\n";
echo cosh(2);   // 3.7621956910836
?>

Notice that cosh(-1) equals cosh(1): feeding in the negative of a number gives the same result.

Common Gotchas

• Radians, not degrees. cosh() does not interpret its argument as degrees. If you have a value in degrees, convert it first with deg2rad().
• Result is never below 1. If you ever get a value less than 1, you are not calling cosh() — you may be confusing it with cos(), whose result ranges from -1 to 1.
• Large inputs overflow. For very large arguments, e^x exceeds the range of a float and PHP returns INF. For example, cosh(1000) is INF.

When to Use cosh()

Reach for cosh() when your math genuinely involves hyperbolic functions: modeling a hanging chain or cable (catenary curves), solving certain differential equations, signal processing, or relativity calculations. For everyday circular trigonometry use cos() instead.

Related Functions

• cos() — the (circular) cosine of an angle.
• sinh() — the hyperbolic sine.
• tanh() — the hyperbolic tangent.
• acosh() — the inverse hyperbolic cosine (undoes cosh()).
• exp() — the exponential e^x, the building block of cosh().

Conclusion

The cosh() function returns the hyperbolic cosine of a number, computed as (e^x + e^-x) / 2. Remember that the input is in radians, the output is always at least 1, and the function is symmetric around zero. When you need ordinary angle-based trigonometry, use cos() instead.

Practice