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

  • Context: Undergrad 
  • Thread starter Thread starter 3uc1id
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
SUMMARY

The integral of Sin(theta)/Sin(theta/2) can be simplified by expressing Sin(theta) in terms of Sin(theta/2). Specifically, using the double angle formula, Sin(theta) can be rewritten as Sin(2*(theta/2)). By applying the identity Sin(x+y) = Sin(x)Cos(y) + Cos(x)Sin(y) with x equal to y, the integration process becomes clearer. The final integration should be evaluated from 0 to π for the complete solution.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the double angle formula.
  • Familiarity with integration techniques in calculus.
  • Knowledge of substitution methods in integral calculus.
  • Basic grasp of the properties of sine functions.
NEXT STEPS
  • Study the double angle formulas for sine and cosine functions.
  • Practice integration techniques involving trigonometric functions.
  • Explore substitution methods in integral calculus.
  • Review the properties of definite integrals, particularly over the interval [0, π].
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus and trigonometry, as well as educators looking for examples of trigonometric integrals.

3uc1id
Messages
7
Reaction score
0
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
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 29 ·
Replies
29
Views
5K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K