Cotangent function and its properties in trigonometry

Cotangent is one of the important trigonometric functions. It can be expressed as the ratio of two sides of a right triangle. The ratio of adjacent to opposite side gives the cotangent of an angle. It can be formulated as cot θ = adjacent / opposite. This shows that cotangent is inverse of tangent i.e. cot θ = 1 / tan θ. To go deeper in the topic, lets learn the way of graphing cotangent functions.

Method of graphing cotangent functions

We will see the process of graphing cotangent function and list out some of the mandatory properties of cotangent function.
graphing cotangent function

The cotangent function graph given above is just opposite to that of tan function and provides vertical asymptote. Some other important properties are listed below.

  • Cotangent function provides inverse results as compared to tangent.

  • The domain of cotangent function includes R i.e. real numbers with an exception of kπ, k being an integer.

  • The period of cot function is π.

  • Cot is an odd function as that of tan.

  • The x-intercept of cotangent is π/2 + kπ.

The values of cotangent function vs cotangent angles are shown in the below table. This values are supposed to be memorized so that they can be used in problems.

θ

00

300

450

600

900

cot θ

Not defined

3

1

1/√3

0

Since tan 0° = 0 and the inverse of zero being undefined, cot 0° is an undefined value. This leads to the fact that since cot 90° is 0, tan 90° will be undefined. Now that you have learned enough on it, lets solve some cotangent function examples.

(1) Evaluate cot(-30°):

The cotangent being an odd function, cot(-30°) = - cot 30° = -√3.

(2) Evaluate cot260 x tan260:

Since cot θ = 1 / tan θ, cot260 x tan260 = cot260 x 1 / cot260 = 1.

(3) Find the cotangent angle if the value of cotangent function is 1/√3:

From the table, we know that cot 60° = 1/√3 which implies that the cotangent angle is equal to 60°.

Now that we have solved the problems, readers are advised to go for practice problems to check their consistency and understanding level of the topic.

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