Plane trigonometry with practical applications, by Leonard E. Dickson.

Ch. XIn GRAPHS, RADIANS, INVERSE FUNCTIONS

153

them draw lines parallel to the horizontal diameter X'X. Choose
any convenient segment OA of X'X to represent 360~, subdivide it into 12 equal parts, label the points of division 30~,
60~,.., 330~, and draw vertical lines through each to intersect
the horizontal line through the point on the circumference with
the same label. The points of intersection are points on the
sine curve.
The abscissas of the points of the circumference marked 0~,
30~,.., 360~ are the line representations of cos 0~, cos 30~,..,
cos 360~. In the lower part of Fig. 85, they have been transferred (by means of parallels to YZ) into the positions of the
horizontal segments extending from equally spaced points on YZ,
labeled 0~, 30~,.., 360~. If we now rotate the page of the book
until YZ becomes horizontal, with Z to the right of Y, we have
a part of the cosine curve in its conventional position (Fig. 86).
g- 90 0~ 90 i180_ 2700~ 60~ 450
FIG. 86. THE COSINE CURVE Y=COS X
Since sin (360~ + x) = sin x, the part of the sine curve y =
sin x from 360~ to 720~ is an exact copy of the part from 0~ to 360~
which is shown at the right of Fig. 85. Similarly for the part
from - 360~ to 0~ (Fig. 87, which is drawn on different scales
from those used in Fig. 85).
- 360\ -18018 soO 6o -- 20
FIG. 87. THE SINE CURVE Y=SIN X
108. The tangent curve. Using the line representation of the
tangent function (Art. 106), we obtain the following construction of part of the tangent curve (Fig. 88):