Integral of Sin(theta)/Sin(theta/2)

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Discussion Overview

The discussion revolves around the integration of the function sin(theta)/sin(theta/2). Participants explore various substitution methods and approaches to simplify the integration process, focusing on trigonometric identities and transformations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) expresses uncertainty about the appropriate substitution for the integral, mentioning an attempt with u=cos(theta/2).
  • One participant suggests rewriting sin(theta) in terms of sin(theta/2) as a potential simplification.
  • Another participant elaborates on this suggestion, indicating that sin(theta) can be expressed using the double angle formula and encourages the OP to apply this approach.
  • The OP later indicates success in solving the integral after integrating over the interval from 0 to pi.

Areas of Agreement / Disagreement

Participants generally agree on the approach of rewriting sin(theta) in terms of sin(theta/2) as a method to facilitate the integration, but the discussion does not resolve the initial uncertainty expressed by the OP regarding substitutions.

3uc1id
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The title says it all. I am trying to integrate that but I am not sure what substitution to use. i tried u=cos(theta/2) but something is not coming out right. does anyone have any suggestions? they would be well appriciated. thanks
 
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Can you write sin(theta) in terms of sin(theta/2)?
 
well, since thw OP hasn't shown up yet, i am going to make it a little bit easier for him.
Like cristo suggested you need to write sin(theta) in terms of sin(theta/2)
notice that sin(theta)=sin(2(theta/2)), now applying the double angle forumula for sin, what do we get?? like sin(x+y) = sin(x)cos(y)+cos(x)sin(y), now apply the same thing here, just notice that in our case we have x=y. Can you go from here??
 
ok tnx. i finally got it but at the end i integrated from 0~pi. to get it.
 

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