Question

Convert (-3, 0) to polar form.

A. (3, 0 degrees)
B. (-3, 180 degrees)
C. (3, 180 degrees)
D. (3, 360 degrees)

Answer 1

To convert the Cartesian coordinates (-3, 0) to polar form, we calculate the radius, resulting in 3, and knowing the point lies on the negative x-axis, we get an angle of 180 degrees. Thus, the polar coordinates are (3, 180 degrees).

Step-by-step explanation:

To convert the Cartesian coordinates (-3, 0) to polar form, we need the distance from the origin to the point, called the radius (r), and the angle (θ) formed with the positive x-axis.

Step 1: Calculate the radius (r) using the Pythagorean theorem for the point (x, y).

1. r = √(x² + y²).
2. For (-3, 0), r = √((-3)² + 0²) = √9 = 3.

Step 2: Find the angle (θ) using the arctangent function. However, because the point is on the negative x-axis, we know that θ should be 180 degrees or π radians.

Thus, the polar coordinates of (-3, 0) are (3, 180 degrees).

The correct answer is C. (3, 180 degrees).