Cot - Tan Formula

The six trigonometric ratios are the ratios of the sides of a right-angled triangle. The Tanθ is the ratio of the altitude, base of the right triangle, and Cotθ is the ratio of the base, altitude of the right triangle. The cot - tan formula presents an inverse relationship between Cotθ and Tanθ.

What is the relationship between Cotθ and Tanθ ?

In this cot - tan formula the two trigonometric ratios of Cotangent and Tangent are inversely related. Tanθ is the ratio altitude and base of a right triangle, and Cotθ is the ratio of the base and altitude of a right triangle.

 Cotθ = 1/Tanθ

Let us try out a few examples to better understand the Cot-Tan Formula.

Solved Examples on Cot - Tan Formula

Example 1: The value of \(Tan \theta = \frac{4}{7} \).  Find the value of \(Cot \theta \).

Solution:

Given \(Tan \theta  = \frac{4}{7} \).

\(\begin{align} Cot\theta &= \dfrac{1}{Tan\theta} \\ &=\dfrac{1}{\frac{4}{7}} \\&= \frac{7}{4} \end{align}\)

Answer: Hence \(Cot \theta = \frac{7}{4} \)

Example 2: The altitude of a right triangle is 9 units and the base of the triangle is 13 units. Find the values of \(Tan \theta \) and \(Cot \theta \).

Solution:

The given Altitude = 9 units and Base = 13 units.

\(Tan \theta = \frac{Altitude}{Base} = \frac{9}{13} \)

\(Cot \theta  = \frac{Base}{Altitude} = \frac{13}{9} \)

Answer: Tanθ = 9/13, Cotθ = 13/9