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