Trig Substitutions Homework: "Uh... why?

  • Thread starter nhmllr
  • Start date
  • Tags
    Trig
In summary, the conversation discusses a step in a larger example problem on trig substitution, where the equations 2/3 *x2 = sin2\theta and \sqrt{}2/3 * x =sin\theta are incorrect and should be \sqrt{2/3} * x = \pm sin (\theta). The person then questions why the derivative of sine is cosine, to which there is no clear answer.
  • #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
 
Physics news on Phys.org
  • #2
What exactly is your question? Why is the derivative of sine, cosine?
 
  • #3
Sourabh N said:
What exactly is your question? Why is the derivative of sine, cosine?

Yeah
 
  • #4
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
 

FAQ: Trig Substitutions Homework: "Uh... why?

Why do we need to do trig substitutions in this homework?

Trig substitutions are a useful tool in solving integrals that involve trigonometric functions. They help simplify the integral and make it easier to solve.

Is there a specific method to follow when doing trig substitutions?

Yes, there are specific rules and formulas to follow when choosing the appropriate trig substitution for a given integral. It is important to understand the rules and practice applying them to different integrals.

Can you explain how to choose the right trig substitution for a given integral?

To choose the right trig substitution, you need to look for a pattern in the integral that matches one of the trigonometric identities. You can also use the Pythagorean identities to help you identify the correct substitution.

Are there any common mistakes to avoid when doing trig substitutions?

One common mistake is forgetting to adjust the limits of integration after making the trig substitution. It is important to always go back and change the limits to match the new variable of integration.

Can you provide an example of a trig substitution in action?

Sure! Let's say we have the integral ∫(x² + 1)^(3/2) dx. We can use the trig substitution x = tanθ to simplify the integral to ∫(secθ)^4dθ. From there, we can use the power rule and trigonometric identities to solve the integral and then substitute back in for x to get the final answer.

Similar threads

Why Is My Argument Calculation for Complex Number Incorrect?
Replies
14
Views
1K
Shape of y = 3x +2 in r - \theta space
2
Replies
45
Views
4K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
Replies
2
Views
2K
Find an equivalent equation involving trig functions
Replies
4
Views
788
I Integration Using Trigonometric Substitution
Replies
8
Views
582
Write ##5-3i## in the polar form ##re^\left(i\theta\right)##
Replies
9
Views
3K
B Question about change of variables
Replies
29
Views
2K
Converting one inverse trig function to another
Replies
4
Views
2K
B Trigonometric substitution, a case I'd like to share
Replies
3
Views
2K
Potential of a rotationally symmetric charge distribution
Replies
4
Views
758

Hot Threads

Recent Insights

Back
Top