Rectangular Coordinates

Rectangular Coordinate:

The rectangular coordinate system otherwise called as Cartesian coordinate system. The rectangular coordinate system is always depends on the grid. In rectangular coordinate every point on the plane can be recognized by the distinctive x and the y coordinates. Now any point on the Earth can be recognized by giving its latitude and the longitude.

Here, o-origin of coordinates, right side value from 0 is point as positive numbers i.e., 1,2,3,etc., left side value called negative numbers -1,-2,-3,....

Problems on Rectangular Coordinates:

Problem 1:

Convert the following polar coordinate to rectangular coordinates R = 5

Angle q =30 degree

Solution:

R = 5 and Angle q = 30

For the given polar coordinates we have to find the equal rectangular coordinate

Where the rectangular coordinates are (x , y)

Here x = R Cos q

And y = R Sin q

So

X = 5 Cos 30

Y= 5 Sin 30

So the rectangular coordinate (4.3301, 2.5)

Problem 2:

Change the given polar coordinate to rectangular coordinates

(R, q) = (5, 53.1)

Solution:

R = 5 and Angle q = 53.1

For the given polar coordinates we have to find the equal rectangular cordinate

Where the rectangular coordinates are (x , y)

Here x = R Cos q

And y = R Sin q

So

X = 5 Cos 53.1

Y = 5 Sin 53.1

So x=3

And y = 4

So the rectangular coordinates are (3, 4)

Problems on Rectangular Coordinates:

Problem 3:

Change the rectangular coordinates to polar coordinates (-3, -7)

Solution:

We know x2 + y2 = r2

So

(-3)2+ (-7)2 = 9 +49 =58

Where q = Tan(y / x )

R2 = 58

R =7.6

Tan q = (-7/-3) =66.8 degrees

So the polar coordinates are (7.6, 66.8)

We can use the same for three dimensional. So we will use x, y, z coordinates.

Let us look at a more wider explanation about the Rectangular Coordinates.
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length

Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin.

One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, one can specify a point in a space of any dimension n by use of n Cartesian coordinates, the signed distances from n mutually perpendicular hyperplanes.