Re: trigonometry sin(pi - x) = sin x

In article <Xns9B749F783F703jamesdowallen@xxxxxxxxxxxx>,
James Dow Allen <gmail@xxxxxxxxxxxxxxxxxxxx> wrote:

ER <ernstras@xxxxxxxxx> might have writ, in news:bd7062aa-e3ee-4d11-
a697-d85bcbe9c062@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

I have a question about the function sin(pi - x) = sin x. It's a bit
confusing.

On the left hand side you have sin(pi - x). Pi is a point on the unit
circle while x is a value on the x axis. How can you subtract a value
on the x axis from a point on the unit circle?

Replace "x" with "theta" and your confusion disappears.

How does this repair "Pi is a point on the unit circle"?

of "x" may have been unfortunate, but variable names tend to be somewhat
arbitrary.

The other answers you received, while not "wrong", missed your point,
I think. Not everyone has the same intuition; you are following the
lead of the famous Francois Vieta, about whom Wikipedia writes:

"Vieta [layed] down the principle that quantities occurring in an
equation ought to be homogeneous, all of them lines, or surfaces, or
solids, or supersolids--an equation between mere numbers being
inadmissible. During the centuries that have elapsed between Vieta's day
and the present, several changes of opinion have taken place on this
subject."

*Angles* should have been included in this sentence about Vieta's
principle. While "changes of opinion have taken place", responders
who insist that pi and x are "just numbers" might wish to repent
and admit the viability of alternate views!

There are no alternate views on this point once the usual modern
assumptions are in place - which are undoubtedly the ones the OP is
working with. Would you argue that Vieta's approach, with its quaint
and complicated proscriptions, is a better set of assumptions?

James Dow Allen
.

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