Plane trigonometry, by S.L. Loney.

48

TRIGONOMETRY.

If it has revolved in the negative direction it has
traced out the negative angle - 135~.
Again, suppose we only know that the revolving line is
in the above position. It may have made one, two, three... complete revolutions and then have described the
positive angle + 225~. Or again it may have made
one, two, three... complete revolutions in the negative
direction and then have described the negative angle
- 135.
In the first case the angle it has described is either
225~, or 360~ + 225~, or 2 x 360~ + 225~, or 3 x 360~ + 225~...... i.e. 225~, or 585~, or 945~, or 1305~....
In the second case the angle it has described is - 135~,
or - 360~ - 135~, or - 2 x 360~ - 1350, or - 3 x 360~ - 135~...... i.e. - 135, or -495~, or -855~, or - 1215....
48. Positive and Negative Lines. Suppose that
a man is told to start from a given milestone on a straight
road and to walk 1000 yards along the road and then to
stop. Unless we are told the direction in which he
started we do not know his position when he stops. All
we know is that he is either at a distance 1000 yards on
one side of 'the milestone or at the same distance on the
other side.
In measuring distances along a straight line it is
therefore convenient to have a standard direction; this
direction is called the positive direction and all distances
measured along it are said to be positive. The opposite
direction is the negative direction and all distances
measured along it are said to be negative.
The standard or positive directions for horizontal lines
is towards the right.