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

[1MileCrash]

Homework Statement

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

 

[Borek]

Are these results different?

 

[1MileCrash]

...apparently.

Why on Earth is that? Which of the umpteen trigonometric identities?

 

[lineintegral1]

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.

 

[SammyS]

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)​

 

[1MileCrash]

Trigonometry really pisses me off sometimes.

 

[Mark44]

If you're working toward a degree in physics and/or math, you had better get a solid handle on trig.

 

[1MileCrash]

I like using it for things like vectors, I just don't like the identities. They feel "synthetic."

 

[Mark44]

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).

 

[cragar]

these identities can be derived using Eulers formula.