Question

What is cot in trigonometry?

Answer 1

Hint: In the given question, we have been asked about the cotangent function. The cotangent is one of the functions of the trigonometry and in a right angled triangle it is equal to the ratio of the adjacent side to the side opposite to the given angle. To explain what is cot function in trigonometry we will need to tell the inverse of cot function, derivation of cot function, reciprocal of cot function.

Complete step by step solution:
The cotangent is one of the functions of the trigonometry and in a right angled triangle it is equal to the ratio of the adjacent side to the side opposite to the given angle. Cotangent function i.e. \[\cot \theta \]tells us the shape of a right angle triangle.
Let us consider the triangle ABC right angled at B

We know that:
\[\cot \theta =\dfrac{base}{perpendicular\ side}\]
Cotangent function of the trigonometry is the reciprocal of the tangent function.
\[\cot \theta =\dfrac{1}{\tan \theta }\]
The cotangent function of any angle is equal to the cosine angle of that function is divided by the sine angle of that function.
\[\cot \theta =\dfrac{\cos \theta }{\sin \theta }\]
In calculus;
The derivation of cotangent function is as follows,
\[\dfrac{d}{d\theta }\cot \theta =-\cos e{{c}^{2}}\theta \]
The inverse of the cotangent function is given by arccot function.
Thus,
Arccot A is equal to or interpreted as the angle whose cotangent is A.


Note: The cotangent graph or the cot function graph is an infinity graph. Cotangent is the reciprocal function of one the three important and basic functions of the trigonometry i.e. tangent function. There are many identities and formulas based on the cotangent function of trigonometry that are formed in trigonometry that can help in finding different values of different functions. The range of the cotangent function belongs to all real numbers.