Sin Cos Tan, why not Sin Sec Tan?

From: Cassandra Thompson (cass.harley_at_bigpond.com)
Date: 07/15/04 

Date: Thu, 15 Jul 2004 02:57:23 GMT

I am learning trigonometry in preperation for actually teaching it.
I am enjoying it, and would like to think I am getting a good
understanding, however I am unsure about hte following.

When talking about highschool level trigonometry we often use
'SOHCAHTOA' as a way to remember that:
Sin@ = O/H
Cos@ = A/H
Tan@ = O/A

Further on we learn that 3 other functions exist that are the inversion
of the first three

CSC@ = H/O
SEC@ = H/A
COT@ = A/O

So that Sin@ = 1/CSC@
        Cos@ = 1/SEC@
        Tan@ = 1/COT@

My question is why is the cofunction of Sin, ie Cosine placed in the
first three that are learnt. Wouldn't it make more sense to group them as

Sin@ = O/H
Sec@ = H/A
Tan@ = O/A

Then introduce the cofunctions
Cos@ = A/H
CSC@ = H/O
Cot@ = A/O

This seems alot more clear to me. Is there some mathematical reason that
I am missing?

Kind Regards,
Cassandra Thompson

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