Question

Convert the rectangular coordinates 0,-5 into polar form. Express the angle using radians in terms of π over the interval 0 ≤ q θ <2 π , with a positive value of r.

Answer 1

To convert rectangular coordinates into polar form, use the formulas r = sqrt(x^2 + y^2) and q = arctan(y/x). For the given coordinates of (0, -5), the polar form is (5, -π/2).

Step-by-step explanation:

To convert rectangular coordinates into polar form, we use the formulas r = sqrt(x^2 + y^2) and q = arctan(y/x).

For the given coordinates of (0, -5), the x-coordinate is 0 and the y-coordinate is -5.

Plugging these values into the formulas, we get r = sqrt(0^2 + (-5)^2) = 5 and q = arctan((-5)/0) = -π/2.

Therefore, the polar form of the coordinates (0, -5) is (5, -π/2).