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 θ 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 θ?
The Greek letter theta (θ) is commonly used to represent an unknown angle in a right triangle. The ACOS function returns the angle θ 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 π/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 2π radians. Half a circle would be π radians (half of 2π). A quarter circle is 2π/4 = π/2 radians. An eighth of a circle is 2π/8 = π/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 / π)
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 is 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 many functions in the 'Math and trigonometry' category.
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