# Cotangent Formula

## What is Trigonometry?

Trigonometry is the branch of mathematics that deals with the relationships between side lengths and angles of triangles. Usually, the triangles taken for trigonometry calculations are right-angle triangles. The trigonometric ratios are six. They are sine, cosine, tangent, cosecant, secant and cotangent and they are usually termed as sin, cos, tan, cosec, sec, cot respectively.

### Tan Cot Formula

The cot tan formulas are reciprocal to each other.  If the length of the adjacent side of the is divided by the length of the opposite side of the gives the value of Cotangent angle in a right triangle. The tan angle is the cot inverse formula.

Cot x Formulas

$Cotx=\frac{AdjacentSide}{OppositeSide}$

$Cotx=\frac{1}{tanx}$

$Tanx=\frac{sinx}{cosx}$

Sec Cosec Cot Formula Relationship

$Cotx=\frac{Cosecx}{Secx}$

Cosec Cot Formula Relationship

1+ cot2 = cosec2

cosec2 - cot2 = 1

Here, the table for calculating the trigonometry formulas for angles are given below. These are commonly used to determine the angle of inclination in the right angle triangle. The trigonometric ratios table is providing the values of trigonometric standard angles such as 0°, 30°, 45°, 60°, and 90°.

## Trigonometric Ratio Table

 Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360° Angles (In Radians) 0° π/6 π/4 π/3 π/2 π 3π/2 2π sin 0 1/2 1/√2 √3/2 1 0 -1 0 cos 1 √3/2 1/√2 1/2 0 -1 0 1 tan 0 1/√3 1 √3 ∞ 0 ∞ 0 cot ∞ √3 1 1/√3 0 ∞ 0 ∞ cosec ∞ 2 √2 2/√3 1 ∞ -1 ∞ sec 1 2/√3 √2 2 ∞ -1 ∞ 1

### Problems Based On Cotangent Formula

Problem 1:  Calculate the cot X, if tan x = 5/6

Solution:

The cotangent formula for calculating cot x using tan x value is 1/tan x

So,

cot x = 15/6

The value of cot x = 6/5

Problem 2: Find the value of in cot. If the length of the adjacent side of the right angle triangle is 6√3cm and the length of the right-angle triangle is 6cm.

Solution:

The cotangent formula for calculating cot is given below.

$Cot\theta =\frac{AdjacentSide}{OppositeSide}$

cot = 6√3 / 6

So, the cot = √3

The value of can be obtained from the trigonometric ratio table.

So, = Cot 30°

1. What is the Function of the Cotangent Formula?

Ans: The classical definition of the cotangent function is ‘the cotangent angle of the right angle triangle shows the ratio of the length of the adjacent side to the length of the opposite side of the right triangle’. This description is valid, only if the values of the right triangle are finite.

2. What is Cotangent Ratio?

Ans: In general cot x formula is the reciprocal of the tan x formula. This means, the ratio of the adjacent side to the opposite side in a right triangle.

3. What is Cotangent on a Calculator?

Ans: According to trigonometry, the cot inverse formula is the tangent. Further, the formula of cotangent is the adjacent side divided by the opposite side of a triangle. For the cotangent equation, the angle in degrees is needed to calculate the exact value.

4. Why is cot 180 Undefined?

Ans: The value for cot 180 degree is undefined. Because the value for sine of a 180-degree angle is zero and the value for sine of a 180-degree angle is 1. So, the value of the cos angle divided by the sine angle is undefined.