This is a free lesson from our course in Trigonometry
This lesson introduces the basic concepts of the polar coordinate with the help of some examples, practice
questions with solution and watching video. It explains how to determine the coordinates
of a point in the polar coordinate system. The equation of a curve expressed in
polar coordinates is known as a polar equation, and a plot of a curve in polar coordinates
is known as a polar plot. Polar coordinate of a point: In the plane we choose a fixed
point 'O', and call it the pole.
Additionally we choose an axis x through the pole and call it the polar
axis. The pole and the polar axis constitute the basis of the polar coordinate system.
(More text below video...)
(Continued from above)
The polar axis is usually drawn in the direction of the positive xaxis.
The pole has been placed at the origin 'O' of a rectangular coordinate system so that the polar axis coincides
with the positive xaxis. Point P has rectangular coordinates
(x, y). Point P can also be located by giving the directed
angle
from the positive xaxis to ray OP at the distancer from the pole to point P. The
ordered pair (r,
) gives the polar coordinates of point.
For example: A point with rectangular coordinates (x, y) has coordinates
(r,
) in polar coordinate
system, where r is the distance from the origin and
is the angle measured counterclockwise from the xaxis to ray drawn from
the origin containing the point (x, y). As this will be a right triangle case, we know that r =
(x^{2}
+ y^{2}),
= tan^{1} (y/x), x = r cos
, y = r sin
.
The point (r,
) is equivalent to
(r,
+
) as (r,
) can also be named
by using the angle formed by the opposite ray and using r instead of r.
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