Re: need help on this problem
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Re: need help on this problem
> Write the following trig expression as an algebraic expression:
>
> sin(arcsin x + arccos x)
Post haste:
start with the addition formula:
sin(A+B) = sinAcosB+sinBcosA
then draw a right triangle with a ration of (opp/hyp = x/1).
Looking at this triangle in light of pythagorus' theorem it is evident that
the other leg has length sqrt(1-x^2) so that
cos(arcsinx)=sin(arccosx)=sqrt(1-x^2)/
Plugging into the addition formula then,
sin(arcsin x + arccos x) = sin(arcsin x)cos(arccos x)+sin(arccos
x)cos(arcsin x) = x^2+(sqrt(1-x^2))^2 =x^2+1-x^2 = 1.
On the other, if there's any justice in the world, then
arccosx+arcsinx = 90 degrees - look at the diagrams again.
geoff
References: