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

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. The choice
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!

James Dow Allen
.

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