Re: More trigonometric equations!!!

On Sat, 31 Jan 2009 01:09:33 -0800 (PST), Albert
<albert.xtheunknown0@xxxxxxxxx> wrote:

Passerby wrote:
If we let  u = tan(x)  and express sin(x) and cos(x) in terms of u,
we find that

   sin(x) = u/sqrt(1+u^2)   and   cos(x) = 1/sqrt(1 + u^2)

What trigonometric identies did you use to derive this?

Draw a right triangle and call one of the acute angles x. Let u be
the length of the side opposite angle x, and 1 be the length of the
side adjacent to angle x. Thus

tan(x) = opposite/adjacent = u/1 = u

The length of the hypotenuse is sqrt(1 + u^2). It is now easy to see
that

sin(x) = opposite/hypotenuse = u/sqrt(1 + u^2)

cos(x) = adjacent/hypotenuse = 1/sqrt(1 + u^2).

.

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