Answer

Verified

382.8k+ views

**Hint:**To solve the question, the concept of trigonometric value should be known. The values of trigonometric values for certain numbers should be known. Details of the trigonometric function is required to solve the question.

**Complete step by step answer:**

To start with some details on the trigonometric function, $\cot $. We know that the trigonometric function $\cot x$ is the reciprocal of the other trigonometric function $\tan x$, this could be mathematically represented as

$\cot x=\dfrac{1}{\tan x}$…………………………………………………………. (i)

On applying the same formula to find value of the given question,

$\Rightarrow \cot {{120}^{\circ }}=\dfrac{1}{\tan {{120}^{\circ }}}$

We know that the value of $\tan x$ for $x$ belonging from $0$ to ${{90}^{\circ }}$ and from ${{180}^{\circ }}$ to ${{270}^{\circ }}$are positive, and for rest of the values of $x$ between $0-{{360}^{\circ }}$ the value of $\tan x$will be negative.

The value of

$\Rightarrow \tan {{120}^{\circ }}$

The angle ${{120}^{\circ }}$ will be written as the complementary angle which is in terms as the sum of ${{90}^{\circ }}$ and ${{30}^{\circ }}$.

$\Rightarrow \tan \left( {{90}^{\circ }}+{{30}^{\circ }} \right)$

Since the function$\tan x$has angle in second quadrant the function will be negative:

$\Rightarrow -\cot {{30}^{\circ }}$

$\Rightarrow -\dfrac{1}{\sqrt{3}}$

On substituting the value of $\tan {{120}^{\circ }}$in the expression$\cot {{120}^{\circ }}=\dfrac{1}{\tan {{120}^{\circ }}}$, so doing this we get:

$\Rightarrow \cot {{120}^{\circ }}=\dfrac{1}{-\dfrac{1}{\sqrt{3}}}$

$\Rightarrow \cot {{120}^{\circ }}=-\sqrt{3}$

**So, the correct answer is “Option D”.**

**Note:**Calculation of the trigonometric function with a certain angle becomes much easier with the help of the graph. Minimum and maximum value of the function could easily be known to us with the help of a graph. The problem could directly be found by a shortcut method.

$\Rightarrow \cot {{120}^{\circ }}=\cot \left( {{90}^{\circ }}+{{30}^{\circ }} \right)$

Since the value of ${{120}^{\circ }}$ is in the second quadrant so the trigonometric function $\tan $ and $\cot $ will give the negative value, so on conversion it becomes:

$\Rightarrow - \tan {{30}^{\circ }}$

The value of $\tan {{30}^{\circ }}$ is $\sqrt{3}$ . So on substituting the value in the above expression we get:

$\Rightarrow - \sqrt{3}$

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

A rainbow has circular shape because A The earth is class 11 physics CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell