Trig Substitutions Homework: "Uh... why?

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Homework Help Overview

The discussion revolves around a problem involving trigonometric substitution, specifically focusing on the relationship between variables and their derivatives in the context of trigonometric functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants express confusion regarding the derivative of a trigonometric function, particularly why the derivative of sine leads to cosine. There are attempts to clarify the relationships between the variables and their derivatives.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the mathematical principles involved. Some have reiterated the original poster's confusion, while others have attempted to redirect the focus towards the fundamental concepts of derivatives in trigonometry.

Contextual Notes

There appears to be a lack of consensus on the interpretation of the original problem setup, with some participants questioning the conclusions drawn from the trigonometric relationships presented.

nhmllr
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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
 
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What exactly is your question? Why is the derivative of sine, cosine?
 
Sourabh N said:
What exactly is your question? Why is the derivative of sine, cosine?

Yeah
 
nhmllr said:

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]

nhmllr said:
[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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