Answer

Verified

438k+ views

**Hint**: Draw the graph of $ \sin x $ and find the range of $ \sin x $ . From the range of $ \sin x $ , we can check which values in the option satisfy the range of $ \sin x $ and which do not. In simple terms, range is the collection of points on the Y-axis from which the graph exists.

**:**

__Complete step-by-step answer__Observe the graph

Given above is the rough sketch of the graph of $ \sin x $ .

From this graph, you can observe a very important thing. That is, the maximum value of $ \sin x $ is $ = 1 $ and the minimum value of $ \sin x = - 1 $

That means, $ \sin x $ can never be greater than one and $ \sin x $ can never be less than minus one.

Mathematically, we can write it as,

$ - 1 \leqslant \sin x \leqslant 1 $ . . . (1)

Now clearly, the values in option (A), (B), (C) are less than one. i.e. they lie in the interval of equation (1) as in all three options, the numerator is less than the denominator. And we know that, if the numerator is less than the denominator then the value of the fraction is always less than one.

Therefore, options (A), (B), (C) are all incorrect.

But option (D) $ \dfrac{5}{4} = 1.25 > 1 $

Thus, $ \sin x $ cannot be equal to this value.

Thus, $ \dfrac{5}{4} $ is not the possible value of $ \sin x $

Therefore, from the above explanation, the correct answer is, option (D) $ \dfrac{5}{4} $

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

**Note**: The key point in this question was knowing the range of $ \sin x $ . If you know the range of $ \sin x $ then you don’t even need to draw the graph to check it. And then the question becomes paperless, as you can directly say that option (D) is the correct answer, just by looking at the options. Therefore, graphs and properties related to graphs are important.

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

Derive an expression for drift velocity of free electrons class 12 physics CBSE

Which are the Top 10 Largest Countries of the World?

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE

The energy of a charged conductor is given by the expression class 12 physics CBSE

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

Derive an expression for electric field intensity due class 12 physics CBSE

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

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

Derive an expression for electric potential at point class 12 physics CBSE