ACOT

Returns the inverse cotangent (the arccotangent) of a number.

Syntax:

ACOT(number)

returns the inverse trigonometric cotangent of number, in other words the angle (in radians) whose cotangent is number. The angle returned is between 0 and PI.To return the angle in degrees, use the DEGREES function.

Example:

ACOT(1)

returns 0.785398163397448 (PI/4 radians).

DEGREES(ACOT(1))

returns 45. The tangent of 45 degrees is 1.

Application:

Surveying and Land Measurement

Imagine a land surveyor who needs to determine the angle of elevation from a point on the ground to the top of a cliff. The surveyor has a measuring device (like a total station or a theodolite) that measures horizontal and vertical distances.

Here's how the ACOT function would be used:

The surveyor sets up their equipment at a known distance from the base of the cliff. This distance is the adjacent side of a right-angled triangle. Let's say this distance is 150 meters.
The surveyor measures the vertical height from the equipment's eye level to the top of the cliff. This height is the opposite side of the triangle. Let's say this height is 200 meters.
The surveyor wants to find the angle of elevation, θ.

The cotangent of the angle θ is given by:

cot(θ)=Adjacent/Opposite

In this case:

cot(θ)=150/200=0.75

To find the angle θ, the surveyor uses the ACOT function:

θ=ACOT(0.75)

Using a calculator, ACOT(0.75)≈0.9273 radians.

To convert this to degrees:

0.9273×180/π≈53.13∘

So, the angle of elevation is approximately 53.13°.

Example Table

A table tracking different measurements for various cliffs could look like this:

	Cliff ID	Horizontal Distance (m)	Vertical Height (m)	Ratio (Adjacent/Opposite)	Angle of Elevation (radians)	Angle of Elevation (degrees)
	A	B	C	D	E	F
1	A	150	200	0.75	0.927295218	53.13°
2	B	100	120	0.833333333	0.876058051	50.2°
3	C	75	300	0.25	1.325817664	75.96°

In this table:

The "Horizontal Distance" is the adjacent side of the triangle.
The "Vertical Height" is the opposite side.
The "Ratio" column is the value of the cotangent.
The "Angle of Elevation (radians)" column is the result of applying the ACOT function to the ratio.
The "Angle of Elevation (degrees)" is the final, more interpretable result.

This example illustrates a practical application of the ACOT function in a field where trigonometric calculations are essential for accurate measurements.