Simplifying Trigonometric Problems | Proven Equations & Solutions

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Homework Help Overview

The discussion revolves around simplifying trigonometric expressions, specifically the expressions 1 + (cos(x)/2) and 1 + cos(x/2). Participants are exploring the nature of simplification in trigonometry and the validity of certain transformations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the clarity of the problem statement and what is meant by "simplify." There is a discussion about the validity of certain derived equations and whether the expressions can be simplified further.

Discussion Status

Some participants have provided feedback on the original poster's attempts, noting potential errors in reasoning and encouraging clarification of the goal of simplification. There is an acknowledgment of the original poster's confusion and a request for further explanation of their approach.

Contextual Notes

The original poster expresses a lack of confidence in their understanding of trigonometry and mentions that their class defines simplification in a specific way. There is a recognition of mathematical errors in the original poster's work, which may have contributed to the confusion in the discussion.

imbroglio
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Homework Statement



Simplify
The problem is either 1+[(cosx)/2]
or
1+[cos (x/2)]

The first one looks unworkable so I'm going with the second...unless any of you see that the first one looks normal...



Homework Equations



I derived/proved some below...

The Attempt at a Solution



1+cos(x/2)
cos^2x=2cos(x/2)-1
cos(x/2)= sqrt [(cos^2x+1)/2]

(1+sqrt [(cos^2x+1)/2])^2

[1+cos^2x+1]/2

(2+cos^2x)/2

[2+cos^2x]/2

[(1-2sin^2x)+2]/2

(1/2)-sin^2x

and now I'm obviously stuck...
Thanks for all your help!
 
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What are you trying to get it to? Simplify can mean a lot of different things when dealing with trig.
 
imbroglio said:

Homework Statement



Simplify
The problem is either 1+[(cosx)/2]
or
1+[cos (x/2)]

The first one looks unworkable so I'm going with the second...unless any of you see that the first one looks normal...
Those are expressions, not "problems". What do you want to do with them? And what do you mean by "is either"? Do you get to choose?



Homework Equations



I derived/proved some below...

The Attempt at a Solution



1+cos(x/2)
cos^2x=2cos(x/2)-1
No, this is clearly untrue when [itex]x= \pi/2[/itex], for example. Perhaps you were thinking of cos(2x)= 2 cos2(x)- 1
cos(x/2)= sqrt [(cos^2x+1)/2
No, [itex]cos(x/2)= \sqrt{(cos(x)+ 1)/2}[/itex]

(1+sqrt [(cos^2x+1)/2])^2

[1+cos^2x+1]/2

(2+cos^2x)/2

[2+cos^2x]/2

[(1-2sin^2x)+2]/2

(1/2)-sin^2x

and now I'm obviously stuck...
Thanks for all your help!
Again, what are you trying to do? If the problem is to simplify either 1+ (cos(x))/2 or 1+ cos(x/2), they both look like they are already about as simple as you are going to make them!
 
Last edited by a moderator:
Sorry for all of the confusion.

Simplify simply means to change the form of the problem to a more "simplified state"...in my class any how.

As you can see I am quite elementary in my trigonometry...however I did manage to simplify the problem...when I have my work with me I might post how I finally finished it.

Thank you for everything and your time, although I am sorry that it took time and that it was impossible for you to help me because my mathematical errors.

Your insight is fantastic. Have a fantastic evening.
 
Last edited:

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