Question

Find all polar coordinates of point P where P = (6, -pi/5)

Answer 1

Answer:

(6 , -π/5 + 2πn) or (-6 , -π/5 + [2n + 1]π) are the polar coordinates of P

answer (b)

Step-by-step explanation:

* Lets study the polar coordinates of a point

- Polar coordinates are written as (r,θ).

- The origin is called the pole, and the x axis is called the polar axis,

 because every angle is dependent on it.

- The angle measurement θ can be expressed in radians or degrees.

- To convert from Cartesian Coordinates (x,y) to Polar

  Coordinates (r,θ):

1. r = √ (x² + y²)

2. θ = tan-1 ( y / x )

- The important difference between Cartesian coordinates and

  polar coordinates.

# In Cartesian coordinates there is exactly one set of coordinates

  for any given point.

# With polar coordinates this isn’t true.

# In polar coordinates there is an infinite number of

  coordinates for a given point.

Ex: The point (5 , π/3) = (5 , −5π/3) = (−5 , 4π/3) = (−5 , −2π/3)

- Look to the attached graph

* If we allow the angle to make as many complete rotations about

 the point (r,θ) can be represented by any of the following

 coordinate pairs.:

# [r , θ + 2πn] or [−r , θ + (2n+1)π],where n is any integer.

* Lets solve your question

∵ P = (6 , -π/5)

∵ r = 6 and Ф = -π/5

∴ The polar coordinates of P are (r , θ + 2πn) or (−r , θ + [2n+1]π)

∴ (6 , -π/5 + 2πn) or (-6 , -π/5 + [2n + 1]π) are the polar coordinates of P