Find intersection of |\cos(x)/2| \text{ and } |\arctan(x)| I want to

jelentetvq

jelentetvq

Answered question

2022-01-26

Find intersection of |cos(x)2|  and  |arctan(x)|
I want to find the intersection for:
|cos(x)2|=|arctan(x)|,  x>0
my attempt: I tried to find the value of x as follows;
cos(x)2=cos(x)sin(x)
Then
1sin(x)=12
csc(x)=12
Then x does not have any answer

Answer & Explanation

saennwegoyk

saennwegoyk

Beginner2022-01-27Added 7 answers

|cosx2| is periodic with period π and attains a maximum of 12, while |tan1x| is strictly incrasing over all R+. Furthermore, we note that |tan1π2|>12 already, whereas |cosx2| is strictly decreasing over (0,π2)
The original equation thus has exactly one positive solution, which does not have an elementary expression; it is the solution of cosx=2tan1x, and is approximately 0.476147.

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