# How to use the ACOS function

**What is the ACOS function?**

The ACOS function calculates the arccosine of a given number.

**What is arccosine?**

The arccosine is the inverse cosine function also written cos^{-1}.

You can find the cos^{-1} on many scientific calculators, the image to the right shows the Win 11 calculator in "scientific" mode.

Press with left mouse button on the image to see the full size.

**What is the inverse cosine?**

The inverse cosine is used to find the angle Î¸ when given the cosine ratio.

**What is the cosine ratio?**

The cosine ratio is the adjacent side divided by the hypotenuse of a right triangle.

cosine = adjacent side / hypotenuse

**What is the angle Î¸?**

The Greek letter theta (Î¸) is commonly used to represent an unknown angle in a right triangle. The ACOS function returns the angle Î¸ expressed in radians.

**What is a right triangle?**

A right triangle is a type of triangle that contains one internal angle measuring 90 degrees or Ï€/2 radians (a right angle).

**What are radians?**

Radians are a unit used to measure angles. An angle of 1 radian has an arc length equal to the circle's radius.

**What is the relationship between the number pi and radians?**

Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2Ï€ multiplied by the circle's radius (2Ï€r).

Since the circumference goes all the way around a circle, that means the full circle measures 2Ï€ radians. Half a circle would be Ï€ radians (half of 2Ï€). A quarter circle is 2Ï€/4 = Ï€/2 radians. An eighth of a circle is 2Ï€/8 = Ï€/4 radians.

Excel has a function that returns the number pi: PI function

**What is an arc?**

An arc is a curved segment of a circle's circumference, it is a portion of the circle's curve, defined by two endpoints.

In other words, an arc is formed by two radii intersecting the circumference and the enclosed edge between them.

**What is a circle's radius?**

The radius of a circle is the distance from the center point to any point on the circle's edge or circumference.

**What is radii?**

The plural form of the word "radius".

**What is the radius of a circle?**

The radius of a circle is the distance from the center point to any point on the circle's edge or circumference.

**What are degrees?**

Degrees are a unit used to measure angles. It is based on dividing a full circle into 360 equal parts. Degrees are divided into fractional parts like minutes and seconds for more precision.

**What is the relationship between radians and degrees?**

The circumference of a circle is 360 degrees or 2Ï€ radians.

360 degrees = 2Ï€ radians

which is

degrees = radians x (180 / Ï€)

Excel has two functions for converting between radians and degrees: RADIANS | DEGREES

## 1. ACOS Function Syntax

ACOS(*number*)

## 2. ACOS Function Arguments

number |
Required. A number equal to or larger than -1 or equal to or less than 1. -1 <= number <= 1. |

The arccosine is the angle whose cosine isÂ *number*. The returned angle is given in radians in the range 0 (zero) to pi.

## 3. ACOS Function example

Formula in cell C3:

## 4. ACOS Function not working

## 5. How to convert the output from ACOS function to degrees?

### Functions in 'Math and trigonometry' category

The ACOS function function is one of 73 functions in the 'Math and trigonometry' category.

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