Question

What is the primary purpose of a "polar to rectangular ordered pairs calculator"?

a) Converting complex numbers to polar form
b) Transforming polar coordinates into rectangular coordinates
c) Calculating the distance between two points in polar coordinates
d) Finding the angle between vectors in polar form

Answer 1

The primary purpose of a "polar to rectangular ordered pairs calculator" is to transform polar coordinates (radius and angle) into their equivalent rectangular (Cartesian) coordinates (x, y).

Step-by-step explanation:

The primary purpose of a polar to rectangular ordered pairs calculator is to transform polar coordinates into rectangular (or Cartesian) coordinates. The polar coordinate system, which specifies points using a radius and an angle, is useful in scenarios involving rotation or circular movement.

However, the rectangular coordinate system, which is defined by orthogonal unit vectors i and j along the x-axis and y-axis respectively, is typically more convenient for describing linear motion. A polar to rectangular calculator would take an input of polar coordinates (r, θ) and output the corresponding rectangular coordinates (x, y) using the relationships x = r*cos(θ) and y = r*sin(θ). When we choose only one option to answer the question about the primary purpose of such a calculator, option b) Transforming polar coordinates into rectangular coordinates is the correct one to mention in the final answer.