Answer:
Equivalent polar coordinates for a point with initial coordinates (9, π/5) can be expressed by adding multiples of 2π to the angle, resulting in (9, π/5 + 2kπ), where k is any integer.
Step-by-step explanation:
To determine all polar coordinates of a point given in Cartesian coordinates or vice versa, we can use the relationships between these two coordinate systems.
In a polar coordinate system, a point P is identified by a pair (r, θ), where r is the radius (distance from the origin) and θ is the angle measured counter-clockwise from the positive x-axis.
For example, given polar coordinates (9, π/5), we can find additional polar coordinates that represent the same point by considering that in polar coordinates, the angle can have infinitely many equivalent values by adding or subtracting multiples of 2π radians (360 degrees).
Therefore, equivalent polar coordinates for the point would be (9, π/5 + 2kπ), where k is any integer.