Arccot Formula
In trigonometry, every function has an inverse. Because this procedure inverses the function, the cotangent becomes the inverse cotangent. When the sides opposite and adjacent to the angles are known, the inverse cotangent is used to calculate the degree value of the angle in the triangle (right-angled).
The Arccot Formula is used in trigonometry, where the cotangent is defined as the ratio of the adjacent side to the opposite side of a certain angle of a right-angled triangle, and the Arccot Formula is the inverse of the cotangent function. The Arccot Formula is also known as cot-1. The Arccot Formula is presented in detail below, along with solved instances.
Arc Functions are inverse trigonometric functions. There is an inverse trigonometric function for every value of a trigonometric function. The inverse trigonometric functions and trigonometric functions operate in opposite directions. It is commonly established that trigonometric functions are particularly useful for right-angle triangles. When two sides of a right triangle are known, the six essential functions are utilised to get the angle. As a result, every trigonometric function has an inverse. The six trigonometric functions are listed below.
Sine
Cosine
Tangent
Secant
Cosecant
Cotangent
These trigonometric functions have the following the Arccot Formula:
inverse sine (or) arcsine
inverse cosine (or) arccos
inverse tangent (or) arctan
inverse secant (or) arcsec
inverse cosecant (or) arccsc
inverse cotangent (or) arccot
Things to learn
Trigonometric and inverse trigonometric functions are useful in many fields, including physics, gardening, construction, and architecture.
The symbol sin-1 x should not be confused with (sin x) -1. Because sin-1 x indicates an angle, the sine of which equals x, the same is true for other trigonometric functions.
The function’s primary value θ is the smallest numerical value of, either +ve or -ve.
Trigonometry was initially studied in ancient India. Ancient Indian mathematicians such as Aryabhatta (476 A.D.), Brahmagupta (598 A.D.), Bhaskara I (600 A.D.), and Bhaskara II (1114 A.D.) discovered major trigonometric conclusions. All of this trigonometric knowledge travelled from India to Arabia and finally to Europe.
The Formula for arccot is:
The basic Arccot Formula can be written as:
θ=arccot(adjacent opposite)
Table values of arccot
The values of arccot are shown in the table below.
| x |
arccot(x) |
arccot(x) |
| -√3 |
5π/6 |
150° |
| -1 |
3π/4 |
135° |
| -√3/3 |
2π/3 |
120° |
| 0 |
π/2 |
90° |
| √3/3 |
π/3 |
60° |
| 1 |
π/4 |
45° |
| √3 |
π/6 |
30° |
Solved Examples
1 If the base of the right-angled triangle DEF is 34 and the height is 22, Find the base angle.
To find: θ
Using the Arccot Formula,
θ=arccot( adjacentopposite)
θ=arccot( 3422)=32.998∘
2 If the base of the right-angled triangle XYZ is 4 and the height is 3, Determine the base angle.
To find: θ
Using the Arccot Formula,
θ=arccot( adjacentopposite)
θ=arccot(43)=36.877∘