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

On Dec 14, 8:40 am, James Dow Allen <gm...@xxxxxxxxxxxxxxxxxxxx>
wrote:
ER <ernst...@xxxxxxxxx> might have writ, in news:bd7062aa-e3ee-4d11-
a697-d85bcbe9c...@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.  The choice
of "x" may have been unfortunate,

I agree that it might be more common here to use a Greek letter,
especially theta, but IMO using "x" is absolutely fine. I wouldn't
call it in any way "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!

This issue is of historical and philosophical interest, but I think is
not one that needs to overly concern a modern student who is just
trying to understand sin(pi - x) = sin x.
.

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