How to use the COSH function
What is the COSH function?
The COSH function calculates the hyperbolic cosine of a number.
What is the hyperbolic cosine of a number?
The hyperbolic cosine is a hyperbolic function defined as:
cosh(x) = (e^x + e^-x)/2
What is e?
The number e is an irrational constant that is approximately equal to 2.71828. It is the base of the natural logarithm function, which is denoted by ln. The natural logarithm function is the inverse of the natural exponential function, which is denoted by ex. This means that if y = ex, then x = ln y.
What is a hyperbole?
Hyperbolic functions are similar to ordinary trigonometric functions, but they use a different shape to define them called hyperbolas.
The chart above shows a hyperbola and two asymptotes (dashed lines) where the intersection is at the center of the hyperbola.
The unit hyperbola looks like this:
It shows x2Â -y2=1 and x2Â -y2=-1
These functions get closer, however, they never crosses or touches these dashed lines (asymptotes).
What are the hyperbolic cosine asymptotes?
The asymptotes of the hyperbolic cosine function are the lines:
- y = +∞
- y = -∞,
This means that the function never crosses or touches these lines, but gets closer and closer to them as x goes to +infinity or -infinity.
What are the main hyperbolic functions, their domain and range?
| Hyperbolic | Domain | Range |
| sinh(x) | All real numbers | (-∞, ∞) |
| cosh(x) | All real numbers | [1, ∞) |
| tanh(x) | All real numbers | (-1, 1) |
| sech(x) | All real numbers | (0, 1) |
What is the hyperbolic domain?
The domain of a hyperbolic function refers to the set of input values it is defined and valid for.
What is the hyperbolic range?
The range of a hyperbolic function refers to the set of possible output values it returns.
| Hyperbolic Function | Formula | Asymptotes |
| sinh | sinh x = (e^x - e^-x)/2 | y = e^x/2 and y = -e^-x/2 |
| cosh | cosh x = (e^x + e^-x)/2 | y = 0 and y = ∞ |
| tanh | tanh x = (e^x - e^-x)/(e^x + e^-x) | y = -1 and y = 1 |
| coth | coth x = (e^x + e^-x)/(e^x - e^-x) | x = nπ and y = -1 and y = 1 |
| sech | sech x = 2/(e^x + e^-x) | y = 0 and y = ∞ |
| csch | csch x = 2/(e^x - e^-x) | x = nπ and y = 0 and y = ∞ |
1. COSH function Syntax
COSH(number)
2. COSH function Arguments
| number | Â Required. Any real number. |
Comments
COSH(n) = (EXP(n)+EXP(-n))/2
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3. COSH function example
Formula in cell C3:
Functions in 'Math and trigonometry' category
The COSH function function is one of many functions in the 'Math and trigonometry' category.
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