Math Problem Statement
Solution
The problem asks to find the polar coordinates of a point with given rectangular (or Cartesian) coordinates , and to express the angle in degrees.
Steps to convert Cartesian coordinates to polar coordinates :
-
Find the radius :
The radius is the distance from the origin to the point, calculated as: For the point : -
Find the angle :
The angle is the counterclockwise angle from the positive -axis to the point. For the point , which lies on the positive -axis, the angle is:
Polar coordinates:
Thus, the polar coordinates of the point are:
Let me know if you'd like more details or have any questions!
Here are five questions that expand on this topic:
- How would you convert Cartesian coordinates to polar form for a point not on the axes?
- What is the relationship between polar and Cartesian coordinates in terms of trigonometry?
- How do you convert polar coordinates back to rectangular (Cartesian) coordinates?
- How would the polar coordinates change for a point in different quadrants?
- What is the significance of the radius 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 .
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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
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