Trig substitutions

  • Thread starter nhmllr
  • Start date
  • #1
nhmllr
185
1

Homework Statement


This is only a step in a bigger example problem on trig substitution
2/3 *x2 = sin2[tex]\theta[/tex]
[tex]\sqrt{}2/3[/tex] * x =sin[tex]\theta[/tex]
[tex]\theta[/tex] = arcsin([tex]\sqrt{}2/3[/tex] * x)
and
x = [tex]\sqrt{}3/2[/tex] * sin[tex]\theta[/tex]
This makes sense
Then I saw
dx / d[tex]\theta[/tex] = [tex]\sqrt{}3/2[/tex] * cos[tex]\theta[/tex]
Uh... why?

Homework Equations


Regular trig equations


The Attempt at a Solution


I have no idea
 

Answers and Replies

  • #2
Sourabh N
631
0
What exactly is your question? Why is the derivative of sine, cosine?
 
  • #3
nhmllr
185
1
What exactly is your question? Why is the derivative of sine, cosine?

Yeah
 
  • #4
36,334
8,293

Homework Statement


This is only a step in a bigger example problem on trig substitution
2/3 *x2 = sin2[tex]\theta[/tex]
[tex]\sqrt{}2/3[/tex] * x =sin[tex]\theta[/tex]
You can't conclude what you have above. This is what it should be.
[tex]\sqrt{2/3} * x = \pm sin (\theta)[/tex]

[tex]\theta[/tex] = arcsin([tex]\sqrt{}2/3[/tex] * x)
and
x = [tex]\sqrt{}3/2[/tex] * sin[tex]\theta[/tex]
This makes sense
Then I saw
dx / d[tex]\theta[/tex] = [tex]\sqrt{}3/2[/tex] * cos[tex]\theta[/tex]
Uh... why?

Homework Equations


Regular trig equations


The Attempt at a Solution


I have no idea
 

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