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

[bobsmith76]

Homework Statement

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

Homework Equations

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?

 

[jedishrfu]

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.

 

[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

 

[SammyS]

Homework Statement

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

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?

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

 

[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.