Purpose
Return value
Syntax
=ACOS(number)- number - The value to get the inverse cosine of. The number must be between -1 and 1 inclusive.
Using the ACOS function
The ACOS function returns the inverse cosine of a value. Input to the arc-cosine function must be between -1 and 1, inclusive. Geometrically, given the ratio of a triangle's adjacent side over its hypotenuse, the function returns the angle of the triangle. For example, given a ratio of 0.5, the function returns an angle of 1.047 radians.
=ACOS(0.5) // Returns 1.047 radians
Convert Result to Degrees
To convert the result from radians to degrees, multiply the result by 180/PI() or use the DEGREES function. For example, to convert the result of ACOS(0.5) to degrees, you can use either formula below:
=ACOS(0.5)*180/PI() // Returns 60 degrees
=DEGREES(ACOS(0.5)) // Returns 60 degrees
Explanation
The graph of ACOS visualizes the output of the function in the range from -1 to 1. ACOS is the inverse of the COS function. However, because COS is a periodic function, the output of ACOS is limited to the range from 0 to π.
Graph courtesy of wumbo.net.
Related functions
COS Function
The Excel COS function returns the cosine of an angle given in radians. To supply an angle to COS in degrees, use the RADIANS function to convert to radians.
ASIN Function
The Excel ASIN function returns the inverse sine of a number.
ATAN Function
The Excel ATAN function returns the inverse tangent of a number. The function is the inverse of TAN.
