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Best answer by Werner_E

Looks like homework, doesn't it?

Where are your attempts in MC15?

What have you already tried?

 

BTW, the condition f(x)>= sine is somewhat strange.
First task should be to make a plot (either by hand or via Mathcad) which shows that you are just looking for the minimum of the part of the curve plotted thick red. Fortunately this minimum (green dot) can be found easily using the zero of the first derivative ...

Werner_E_0-1715567331610.png

 

The name "arctg" is quite outdated and should no longer be used according to the current standard (ISO 80000-2)

 

Werner_E_1-1715566869933.png

In Mathcad this function is called "atan".

 

2 replies

W
Werner_E25-Diamond IAnswer
25-Diamond I
May 13, 2024

Looks like homework, doesn't it?

Where are your attempts in MC15?

What have you already tried?

 

BTW, the condition f(x)>= sine is somewhat strange.
First task should be to make a plot (either by hand or via Mathcad) which shows that you are just looking for the minimum of the part of the curve plotted thick red. Fortunately this minimum (green dot) can be found easily using the zero of the first derivative ...

Werner_E_0-1715567331610.png

 

The name "arctg" is quite outdated and should no longer be used according to the current standard (ISO 80000-2)

 

Werner_E_1-1715566869933.png

In Mathcad this function is called "atan".

 

T
TT_110567826-ContributorAuthor
6-Contributor
May 22, 2024

And how do you find the solution of it?

W
Werner_E25-Diamond I
25-Diamond I
May 22, 2024
@TT_11056782 wrote:

And how do you find the solution of it?

As already written - define the first derivative of the function, set it to zero and solve for x. The plot suggests that you have to look in the range from pi to 2*pi.

Fortunately the position you arrive at is within the intervals of interest. Otherwise you would have to examine the endpoints of the curve fragments of interest.

 

Give it a try! Set up a worksheet, define the function f, define its derivative and use the "root" function or a solve block with "find" to find the solution in the range (pi; 2 pi). Don't use the symbolic "solve" as it would not be able to find a solution.

If you experience a problem while working with Mathcad, come back here, ask your question and don't forget to attach your worksheet.

V
vnamboodheriCommunity Manager
Community Moderator
May 16, 2024

Hello @TT_11056782, 

 

It looks like you have a response from a community member. If it helped you solve your question please mark the reply as the Accepted Solution. 

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Thanks,
Community Moderation Team.

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