Question

Plot the point given in polar coordinates, and find other polar coordinates (r, θ) of the point for which.

(a) r > 0,  - 2π  ≤  θ  < 0         (b) r < 0,   0 ≤ θ < 2π          (c) r > 0,     2π  ≤  θ  <  4π

(5, 2π/3)

Answer 1

Step 1 :

The point in polar co-ordinates is .

Steps to plot the point :

1. First draw a ray with an angle .

2. Then go out a distance of 5 units along the ray and plot the point .

Graph of the point .

Solution :

Graph of the point is

Answer 2

(a)

Step 1 :

The condition for the point in the polar coordinate is .

The point in polar co-ordinates is .

In the polar coordinates we can represent the point in multiple representations of a point.

The point can also be represented as .

Subtract from the angle (Where k =1).

Solution :

Answer 3

(b)

Step 1 :

The condition for the point in the polar coordinate is .

The point in polar co-ordinates is .

In the polar coordinates we can represent the point in multiple representations of a point.

The point can also be represented as .

Add half revolution ( radians ) to the angle and replace by (Where k = 0).

Solution :

.

Answer 4

(c)

Step 1 :

The condition for the point in the polar coordinate is .

The point in polar co-ordinates is .

In the polar coordinates we can represent the point in multiple representations of a point.

The point can also be represented as .

Add one revolution ( radians ) to the angle (Where k = 1).

Solution :

.