Plane trigonometry, by S.L. Loney.

12

TRIGONOMETRY.

The student must notice this point carefully. If the
unit, in terms of which the angle is measured, be not
mentioned, he must mentally supply the word "radians."
Otherwise he will easily fall into the mistake of supposing
that wr stands for 180~. It is true that 7r radians (7rC) is
the same as 180~, but wr itself is a number, and a number
only.
19. To convert circular measure into sexagesimal
measure or centesimal measure and vice versa.
The student should remember the relations,
Two right angles = 180~ = 200 g = r radians.
The conversion is then merely Arithmetic.
Ex. (1) 45w7= '45 x 180~=81~= 90s.
3 3 3
(2) 3C- x 7 = 3 x 180~= - x 200g.
7r 7r 7r
(3) 40~ 15' 36" = 40~ 15' = 40-26~
=40-26 x 0 — = 22367r radians.
180
(4) 40 15' 36" =401536g=40-1536 x radians
200
= 2007687r radians.
20. Ex. 1. The angles of a triangle are in A. P. and the number of
grades in the least is to the number of radians in the greatest as 40: 7r;
find the angles in degrees.
Let the angles be (x-y)O, x~, and (x + y)~.
Since the sum of the three angles of a triangle is 180~, we have
180=x - y +x +x +y = 3x,
so that x = 60.
The required angles are therefore
(60- y)0, 60~, and (60 + y).
Now (6 0 - )~= x(60 -),
Now (60 - y) = - x (60 - y)9,
9

and

(60 + y)~ = x (60 + y) radians.
180