# Is wolfram wrong?

1. Sep 26, 2011

### 1MileCrash

1. The problem statement, all variables and given/known data

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

2. Sep 26, 2011

### Staff: Mentor

Are these results different?

3. Sep 26, 2011

### 1MileCrash

...apparently.

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

4. Sep 26, 2011

### lineintegral1

They are the same. This is the double angle formula for sine.

5. Sep 26, 2011

### SammyS

Staff Emeritus
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)​

6. Sep 26, 2011

### 1MileCrash

Trigonometry really pisses me off sometimes.

7. Sep 26, 2011

### Staff: Mentor

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

8. Sep 26, 2011

### 1MileCrash

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

9. Sep 26, 2011

### Staff: Mentor

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. Sep 26, 2011

### cragar

these identities can be derived using Eulers formula.