This is a free lesson from our course in Trigonometry
In this lesson, you'll learn the basics and explanation on how to convert rectangular coordinates to polar coordinates, and vice-versa. Rectangular coordinates
and polar coordinates are two different ways of using two numbers to locate a point
on a plane. Rectangular coordinates are in the form (x, y), where
'x' and 'y' are the horizontal and vertical distances from the origin. Polar coordinates
are Polar coordinates are in the form: ( r ,),
where 'r' is the distance from the origin to the point, and ''
is the angle measured from the positive 'x' axis to the point. (More text below video...)
(Continued from above) The rectangular coordinates can be converted to the polar
coordinates by using the formulas r =
(x2
+ y2) and
= tan-1 (y/x),
For example, to convert (-3, 3) to polar coordinates, r =
(x2
+ y2) =
((-3)2
+ 32) = 32
and
= tan-1 (y/x) = tan-1 (3/(-3)) = -/4.
So the polar coordinates in this case are (-32,
-/4) or (32,
3/4).
The polar coordinates can be converted to the rectangular coordinates by using the
formulas x = r cos
and y = r sin
.
For example, to convert the polar coordinates (4,
/3) to rectangular coordinates,
plug-in the values in the formulas x = r cos
= 4 cos
/3 = 2 and y
= r sin
= 4 sin
/3 = 23.
So the rectangular coordinate in this case is (2, 23).
Once you go through the instructor's explanation in the video which brings in an
element of real-class room experience and practice questions with solution, it'll
be easy for you to understand and will help in problem solving.
Let us see one more example :
Convert the rectangular coordinates (1 , 1) to polar coordinates to three decimal
places. Express the polar angle
in degrees and radians.
You first find r using the formula
r =
(x 2
+ y 2) for the point (1 , 1).
r =
(x 2
+ y 2) =
[1 + 1] =
( 2 )
You now find tan
using the formula tan
= y / x.
tan
= 1 / 1
Using the tan-1 function, we obtain
=
/ 4 or t = 45
Point (1 , 1) in rectangular coordinates may be written in polar for as follows
:
(
2 ,
/ 4 ) or (
2 , 45
)
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),
where 'r' is the distance from the origin to the point, and '
(x2
+ y2) and
/4.
So the polar coordinates in this case are (-3