"Wolfram's Derivative of (sin x)^2: Is it Correct?

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Homework Help Overview

The discussion revolves around the derivative of the function (sin x)^2, specifically addressing a claim made by Wolfram that the derivative is sin(2x). Participants are questioning the validity of this claim and exploring the relationship between different trigonometric identities.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are examining whether the derivative provided by Wolfram and the derivative derived using the product rule (2(sin x)(cos x)) are equivalent. There is a focus on understanding the underlying trigonometric identities that relate these expressions.

Discussion Status

Some participants have noted that the two expressions are indeed equivalent through the double angle formula for sine. However, there is ongoing exploration of the implications and understanding of these identities, with no explicit consensus reached on the broader context of their application.

Contextual Notes

Participants express frustration with trigonometric identities and their perceived complexity, indicating a potential barrier to understanding. There is also mention of the necessity of mastering these concepts for those pursuing degrees in physics or mathematics.

1MileCrash
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Homework Statement



Wolfram says the derivative of (sin x)^2 is sin2x. Shouldn't it be 2(sin x)(cos x)?
 
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Are these results different?
 
...apparently.

Why on Earth is that? Which of the umpteen trigonometric identities?
 
1MileCrash said:

Homework Statement



Wolfram says the derivative of (sin x)^2 is sin2x. Shouldn't it be 2(sin x)(cos x)?

They are the same. This is the double angle formula for sine.
 
sin(2x) = 2 sin(x) cos(x)

You can get this from sin(2x) = sin(x + x)
= sin(x) cos(x) + cos(x) sin(x)

= 2 sin(x) cos(x)​
 
Trigonometry really pisses me off sometimes.
 
If you're working toward a degree in physics and/or math, you had better get a solid handle on trig.
 
I like using it for things like vectors, I just don't like the identities. They feel "synthetic."
 
1MileCrash said:
I like using it for things like vectors, I just don't like the identities. They feel "synthetic."
Synthetic?

The identities are there to help you out. In your other current post, you put in a lot more work than was necessary, by not using a fairly simple identity: cos(2x) = cos2(x) - sin2(x).
 
  • #10
these identities can be derived using Eulers formula.
 

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