These formulas might have been immediately deduced from the group (9), by

changing ab into a, ab into b, a into

13. The following are various forms of expressing the principles deduced from Art. 14 to Art. 31 inclusive.

* All the infinities in the above table should perhaps strictly have the doubtful sign,

since they are the transition value.

14. The following are the most useful general relations of arcs or angles deduced in the preceding pages, or deducible from the formulas which they contain.

{ (2n + 1) 180°

-a

-a}

or sec (2n 1800 a)

The formulas of Trigonometry may be varied to almost any extent, and the same quantity expressed in many different ways.

15. The following, of less frequent occurrence, may be readily deduced from the above.

sin (a+b)

cos a cos b

sin (a + b)

=

sin a sin b

is the base of the Naperian system of logarithms. For the demonstration of the first two of these four formulas see next article.

15. The following will be found a useful table of reference.

-1

* Arc (siny) or sin

y are read the arc whose sin is y.