Final answer:
To convert the Cartesian coordinates (-4, -4) to polar coordinates, calculate the radial distance using the Pythagorean theorem, resulting in 4√2 meters, and then determine the angle, which is 225° or 5π/4 radians.
Step-by-step explanation:
Converting Cartesian Coordinates to Polar Coordinates
The student asked how to convert the point with cartesian coordinates (-4, -4 3) to polar coordinates. Note that there seems to be a typo in the question; the correct format for Cartesian coordinates in 2D is (x, y). Assuming the coordinates are actually (-4, -4), the conversion to polar coordinates involves two steps: calculating the radial coordinate (r) and the angle (θ).
To find the radial coordinate, also known as the distance to the origin in a polar coordinate system, use the Pythagorean theorem:
r = √(x² + y²)
r = √((-4)² + (-4)²)
r = √(16 + 16)
r = √32
r = 4√2 meters
To find the angle θ, you would typically use the arctan function:
θ = arctan(y/x)
But in this case, since x and y are equal and negative, θ is 225° or 5π/4 rads (in the third quadrant).
Thus, the polar coordinates are (4√2, 5π/4).