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.

**RADIUS: **The distance from the pole is termed as the radial coordinate or radius

**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 and*b* 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)

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.

2. used in navigation

In the next session we will discuss about Standard Equation of a Line and You can visit our website for getting information about algebra word problems and physics notes for class 12 cbse.