Math Problem Statement

A point is graphed in rectangular form. Find polar coordinates for the point, with r > 0 and 0 ≤ 𝜃 < 2𝜋. (r, 𝜃) =

Solution

To find the polar coordinates (r,θ)(r, \theta) of a point in rectangular form, we use the following formulas:

  1. r=x2+y2r = \sqrt{x^2 + y^2} (distance from the origin).
  2. θ=tan1(yx)\theta = \tan^{-1}\left(\frac{y}{x}\right) (angle with the positive x-axis, adjusted for quadrant).

Let me know the coordinates of the point in rectangular form (e.g., (x,y)(x, y)), and I can calculate the polar coordinates for you.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Polar Coordinates
Trigonometry

Formulas

r = √(x² + y²)
𝜃 = tan⁻¹(y/x) (adjusted for the quadrant)

Theorems

Pythagorean Theorem
Inverse Tangent Function

Suitable Grade Level

Grades 9-12