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Question

Answers

$

{\text{A}}{\text{. }}\left( {0,\dfrac{\pi }{2}} \right) \\

{\text{B}}{\text{. }}\left( {\dfrac{\pi }{2},\pi } \right) \\

{\text{C}}{\text{. }}\left( {\pi ,\dfrac{{3\pi }}{2}} \right) \\

{\text{D}}{\text{. }}\left( {\dfrac{{3\pi }}{2},2\pi } \right) \\

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Answer
Verified

Given Data,

Range of x = [0, 2π]

Graphs of sin x and cos x.

In order to study the graph of sin x and cos x we plot them on the XY – axis within the limits of x = [0, 2π]

It is shown as follows:

The graphs of trigonometric functions sin x and cos x look as per the given figure. We can verify the correctness of the graph obtained by substituting the values of x in the function it satisfies for every single value of x in the range [0, 2π].

From the figure, we can say that in between the interval starting from π/2 till π, both the graphs of sin x and cos x appear to be coming closer than zero, i.e. their value is decreasing.

In all the other intervals of them in between [0, 2π] they are either increasing or only one of them is decreasing.

Hence, for x greater than or equal to zero and less than or equal to 2 pi, sin x and cos x are both decreasing on the intervals $\left( {\dfrac{\pi }{2},\pi } \right)$.

The graphs of sin and cos trigonometric functions are defined for all real numbers and continuous for all the values of x.

Sin and cos functions are also periodic, i.e. the distance between two consecutive maxima in a sine or a cos function graph is regular throughout its entire course and is equal to 2π.