Plane trigonometry, by S.L. Loney.

TANGENT-CURVE.

61

Since the tangent of an angle slightly greater than a
right angle is negative and almost infinitely great, the. / Y /L /
/Y I
R/'RE R2F'/ P Ri,R2 R3x
L
dotted curve immediately beyond LR1L' commences at an
infinite distance on the negative side, i.e. below, OX.
The Tangent-Curve will clearly consist of an infinite
number of similar but disconnected portions, all ranged
parallel to one another. Such a curve is called a Discontinuous Curve. Both the Sine-Curve and the CosineCurve are, on the other hand, Continuous Curves.
*65. Cotangent-Curve. If the curve to represent
the cotangent be drawn in a similar manner, it will be
found to meet 0 Y at an infinite distance above 0; it will
pass through the point R, and touch the vertical line
through R2 at an infinite distance on the negative side of
OX. Just beyond R2 it will start at an infinite distance
above R2, and proceed as before.
The curve is therefore discontinuous and will consist
of an infinite number of portions all ranged side by side.