Math Problem Statement

Find the polar coordinates of the point with rectangular coordinates (1, 0). Express the angle in degrees.

Solution

The problem asks to find the polar coordinates of a point with given rectangular (or Cartesian) coordinates (1,0)(1, 0), and to express the angle in degrees.

Steps to convert Cartesian coordinates (x,y)(x, y) to polar coordinates (r,θ)(r, \theta):

  1. Find the radius rr:
    The radius rr is the distance from the origin to the point, calculated as: r=x2+y2r = \sqrt{x^2 + y^2} For the point (1,0)(1, 0): r=12+02=1=1r = \sqrt{1^2 + 0^2} = \sqrt{1} = 1

  2. Find the angle θ\theta:
    The angle θ\theta is the counterclockwise angle from the positive xx-axis to the point. For the point (1,0)(1, 0), which lies on the positive xx-axis, the angle is: θ=0\theta = 0^\circ

Polar coordinates:

Thus, the polar coordinates of the point (1,0)(1, 0) are: (1,0)(1, 0^\circ)

Let me know if you'd like more details or have any questions!


Here are five questions that expand on this topic:

  1. How would you convert Cartesian coordinates to polar form for a point not on the axes?
  2. What is the relationship between polar and Cartesian coordinates in terms of trigonometry?
  3. How do you convert polar coordinates back to rectangular (Cartesian) coordinates?
  4. How would the polar coordinates change for a point in different quadrants?
  5. What is the significance of the radius rr being negative in polar coordinates?

Tip: When converting between Cartesian and polar coordinates, always make sure to check the quadrant to determine the correct angle θ\theta.

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Math Problem Analysis

Mathematical Concepts

Polar Coordinates
Cartesian Coordinates
Trigonometry

Formulas

r = sqrt(x^2 + y^2)
theta = arctan(y/x)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-11