## Polar Equations of Lines

Previously we have discussed about linear equations calculator and In today’s session we are going to discuss about Polar Equations of Lines,

WHAT IS COORDINATE SYSTEM?

Coordinate system is used for determining a point in space. It uses 2 or more values to determine a point.

Coordinate system may be

1. Cartesian coordinate system(x,y)

2. Polar coordinate system(r,θ )
DEFINATION OF POLAR COORDINATES SYSTEM:

• A two-dimensional coordinate system is polar coordinate system
• In polar coordinate system, each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. (want to Learn more about Polar Equations, click here),

POLE: The fixed point in coordinate system is called the pole.

POLAR AXIS: the ray from the pole in the fixed direction is the polar axis.

EQUATION OF A LINE
y= mx + b

m, b are constants . m is the slope and b is the intercept on y axis
Polar Equations of Lines

r = (m*rcos θ + b)/sin θ

where m is the slope of the line andb is the y-intercept. When θ = 0, the graph will be indeterminate.

Let us see how to convert the polar to Cartesian co-ordinate and vice versa.
It can be done by the following expressions:
sin (θ) = [y/r]
cos (θ) = [x/r]

Therefore,
x= r cos (θ)
y=r sin (θ)

EXAMPLE :
Problem 1:   Solve the polar coordinates (6, 90°) into Cartesian coordinates

Solution:

Change the polar into Cartesian form
Here, r = 6 and θ = 90°
x = r cos (θ)
y = r sin (θ)
x = 6 cos 90°= 6 × 0
x = 0
y = 6 sin 90°
= 6x 1
y = 6
Cartesian form is (0, 6)
Uses of Polar Coordinates

1. used in astronomy for finding the circular and orbital motion of many things in universe.