The rectangular and polar coordinates of a

point are (x, y) and (r, θ), where x = 4 and
θ = 38◦
.
Determine the value of r.

To find the value of r (the magnitude or radial distance from the origin) given the rectangular coordinates (x, y) and the polar coordinate (r, θ), we use the distance formula in the Cartesian plane.

The distance formula is:
d = √((x - a)^2 + (y - b)^2)
where (x, y) is the point's rectangular coordinates, and (a, b) is the origin's coordinates (0, 0).

In this case, we are given the x-coordinate as x = 4. Since the point is in the Cartesian plane, the y-coordinate is not given, but let's assume it's y = 0 for simplicity.

Plugging these values into the distance formula, we have:
d = √((4 - 0)^2 + (0 - 0)^2)
= √(16 + 0)
= √16
= 4

Therefore, the value of r is 4 units.