Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec 4] Geometrical and Mechanical Applications of the Deriiative 61
segments (Fig. 13):
Since KM = \y \ and
t = TM is the so-called segment of the tangent,
S t = TK is the subtangent,
n NM is the segment of the normal,
S n = KN is the subnormal.
S t
Fig. 13
/f Sn N X
tan y = y'Q , it follows that
j/o
4. Segments associated with the tangent and the normal in a polar systern
of coordinates. If a curve is given
in polar coordinates by the equation
r = /(q>), then the angle u.
formed by the tangent MT and the
radius vector r OM (Fig. 14), is . \Af
defined by the following formula:
The tangent MT and the normal MN
at the point M together with the radius
vector of the point of tangency
and with the perpendicular to the
radius vector drawn through the pole
determine the following four segments
(see Fig. 14):
Fig. 14
t = MT is the segment of the polar tangent,
n = MN is the segment of the polar normal,
S t = OT is the polar subtangent,
S n = ON is the polar subnormal.