Find all polar coordinates of point p where p = (9, pi divided by 5).

Solution:

Given, the point p = (9,pi divided by 5).

We have to find all the polar coordinates of point P.

Both the problem and the solution can be summarized in the diagram below:

The given coordinate P, is of the form P(r, Ɵ). Where r = 9 and Ɵ = π/5. The quadrant space above below shows point P’, P’’, and P’’’ which are the corresponding polar coordinates and they are as follows:

1) P’ = (9, 4π/5)

2) P’’ = (-9, 6π/5)

3) P’’’= (-9, 9π/5)

The value of r is negative below the horizontal axis and that is why the r coordinate in P’’ and P’’’ is negative i.e. -9.

Find all polar coordinates of point p where p = (9, pi divided by 5).

Summary:

The polar coordinates of point p where p = (9, pi divided by 5) are:P(9, π/5), P’(9, 4π/5), P’’(-9, 6π/5) and P’’’(-9, 9π/5).