Purpose
Return value
Syntax
=COS(number)
- number - The angle in radians for which you want the cosine.
Using the COS function
The COS function returns the cosine of an angle provided in radians. In geometric terms, the cosine of an angle returns the ratio of a right triangle’s adjacent side over its hypotenuse. For example, the cosine of PI()/6 radians (30°) returns the ratio 0.866.
=COS(PI()/6) // Returns 0.886
Using Degrees
To supply an angle to COS in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians. For example, to get the COS of 60 degrees, you can use either formula below:
=COS(60*PI()/180)
=COS(RADIANS(60))
Explanation
The graph of cosine above visualizes the output of the function for all angles from 0 to a full rotation. Geometrically, the function returns the x -component of the point corresponding to an angle on the unit circle. Since the cosine of an angle returns a ratio, the output of the function will always be in the range [-1, 1].
Graph courtesy of wumbo.net
Purpose
Return value
Syntax
=COSH(number)
- number - The hyperbolic angle.
Using the COSH function
The Excel COSH function returns the hyperbolic cosine of a number, which represents a hyperbolic angle . Given the input of 1, the function returns the value 1.543080635.
=COSH(1) // returns 1.543080635
Explanation
The hyperbolic cosine function returns the horizontal component of the point on the right branch (x ≥ 1) of the unit hyperbola corresponding to the hyperbolic angle given as input.
Together with the hyperbolic sine function , the functions parameterize the right branch of the unit hyperbola given by the equation x² - y² = 1. In plain language, this means that the two functions trace out the shape of the right branch of the unit hyperbola. Given a hyperbolic angle corresponding to a point on the hyperbola’s curve, COSH returns the horizontal component of the point, while SINH returns the vertical component of the point.
For example, given the hyperbolic angle -1, hyperbolic cosine returns the x-component 1.543080635, and hyperbolic sine returns the y-component -1.175201194.
Here is a table that shows some points on the unit hyperbola formed by COSH and SINH.
As the value of the hyperbolic angle gets larger, the horizontal component diverges to infinity. This is different from the circular cosine function , which is periodic and repeats values.
Images courtesy of wumbo.net .
