Trig Substitutions Homework: "Uh... why?

[nhmllr]

Homework Statement

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

Homework Equations

Regular trig equations

The Attempt at a Solution

I have no idea

 

[Sourabh N]

What exactly is your question? Why is the derivative of sine, cosine?

 

[nhmllr]

What exactly is your question? Why is the derivative of sine, cosine?

Yeah

 

[Mark44]

Homework Statement

This is only a step in a bigger example problem on trig substitution
2/3 *x² = sin²\theta
\sqrt{}2/3 * x =sin\theta

You can't conclude what you have above. This is what it should be.
\sqrt{2/3} * x = \pm sin (\theta)

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

Homework Equations

Regular trig equations

The Attempt at a Solution

I have no idea