# Trigonometric functions like sin(2x)=2sin(x)cos(x)

1. Mar 20, 2006

### TheDestroyer

Hi guyz, as we know we have some known relations in the trigonometric functions like

sin(2x)=2sin(x)cos(x) and sin(x/2)=1/2-1/2 cos2x

My question is are there similiar formulas for arcsin and arccos?

I know those only !

arcsin x =ln(ix-sqrt(1-x^2))
arccos x =ln(-ix-sqrt(1-x^2))

I'm working in electrodynamics, and i reached an integral for the kinetic energy and the answer should be mc^2-mc^2, but i'm getting arcsin !!

i knew the answer already about the energy, but i don't this i should neglect the problem of the damn inverse function,

Can any one help and tell me some formulas?

Thanks...

2. Mar 22, 2006

### arildno

You are not getting "arcsin"; you might be getting the arcsine to some argument. What argument?

3. Mar 23, 2006

### uart

"sin(x/2)=1/2-1/2 cos2x"

That's not correct. Perhaps the identity you were thinking of was
sin^2(x)=1/2-1/2 cos2x.

I'm not really sure what your question is but you haven't fogotten about the trig of arc_trig relationships have you? I mean like cos(arctan(x)) = 1/sqrt(1+x^2) etc.

Last edited: Mar 23, 2006
4. Mar 23, 2006

### mathwonk

i suppose you could take a formula like sin(2x) = 2sin(x)cos(x), set u = sinx, cosx = sqrt(1-u^2), x = arcsin(u), and apply arcsin to the previous formula,

to get say 2arcsin(u) = arcsin(2u[sqrt(1-u^2)]).

seems pointless though. i.e. any formula for sin, cos, IS a formula for arcsin, arccos.

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