# What's the difference between sin^2(x) and sin(x^2)?

1. Jan 25, 2012

### bobsmith76

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

what's the difference between sin^2(x) and sin(x^2)?

2. Relevant equations

3. The attempt at a solution

I can't do sin^2(x) on the calculator. let's just use sin(25) as an example, what's the difference?

2. Jan 25, 2012

### Staff: Mentor

first expression is sin(x) times sin(x) so you'd enter it as ( sin(x) ) ^ 2 and your calculator should be able to evaluate it.

3. Jan 25, 2012

### iRaid

$sin^{2}x = sinxsinx$
The other 1 is just squaring the x not the whole function.

Also on a side note,
$sinx+sinx = 2sinx$

4. Jan 25, 2012

### SammyS

Staff Emeritus
Indeed. if x = 5, sin2(x) ≈ 0.919536, whereas sin(x2) ≈ -0.132352

5. Jan 25, 2012

### epenguin

sin2x MEANS (sin x)2.

Which you can calculate on your calculator.

IMHO you are not the only one and not totally at fault to be confused - sin2x as far as I can see is a sort of mathematical slang, not strictly logical (so no wonder your calculator doesn't understand it either) which by its antiquity is let through and is universal - so there it is to get used to.