Answer:
D. [tex]\pi<x<2\pi[/tex]
Step-by-step explanation:
Given the function
[tex]y=cosx[/tex]
Kindly refer to the graph attached in the answer area.
Referring to the intervals [0, [tex]2\pi[/tex]].
It decreases from the interval [0, [tex]\pi[/tex]] and then starts increasing in the interval
[tex][\pi,2\pi][/tex].
Proving by taking derivative:
Taking derivative of the function, [tex]y=cosx[/tex]
[tex]\dfrac{dy}{dx}=-sinx[/tex]
In the interval [tex][\pi,2\pi][/tex], [tex]sinx[/tex] is negative i.e. [tex]sinx<0[/tex].
Therefore [tex]-sinx>0[/tex]
When, the derivative of a function is positive, then the function is strictly increasing.
So, the answer is:
D. [tex]\pi<x<2\pi[/tex]
