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