77.2k views
5 votes
Convert the point with cartesian coordinates (-4, -4 3) to polar coordinates

1 Answer

1 vote

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).

User Ali Rasouli
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories