Cotangent Formula

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. 

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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 

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°