# Trig substitutions

## 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

Related Precalculus Mathematics Homework Help News on Phys.org
What exactly is your question? Why is the derivative of sine, cosine?

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

Mark44
Mentor

## 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

I have no idea