-in-polar-coordinates.jpeg "(0 1) In Polar Coordinates")
Understanding (0, 1) in Polar Coordinates
Polar coordinates provide an alternative way to represent points in a two-dimensional plane. Instead of using Cartesian coordinates (x, y), polar coordinates use distance from the origin (r) and angle from the positive x-axis (θ).
Converting from Cartesian to Polar Coordinates
To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), we use the following formulas:
- r = √(x² + y²)
- θ = arctan(y/x)
Analyzing (0, 1) in Polar Coordinates
Let's analyze the point (0, 1) in Cartesian coordinates. To convert it to polar coordinates:
- r = √(0² + 1²) = 1
- θ = arctan(1/0) = π/2
Therefore, the polar coordinates of (0, 1) are (1, π/2).
Understanding the Result
- r = 1 indicates that the point is one unit away from the origin.
- θ = π/2 indicates that the point lies on the positive y-axis, making an angle of 90 degrees (or π/2 radians) from the positive x-axis.
This means the point (0, 1) in Cartesian coordinates is equivalent to the point (1, π/2) in polar coordinates. This point is located on the unit circle, at the topmost point.
Key Takeaways
- The point (0, 1) in Cartesian coordinates is represented as (1, π/2) in polar coordinates.
- Polar coordinates provide a different perspective on points in a plane, using distance and angle instead of horizontal and vertical positions.
- Understanding the conversion between Cartesian and polar coordinates allows you to represent points in various ways and solve problems in different contexts.