-to-polar-form.jpeg "(-3 3) To Polar Form")
Converting Rectangular Coordinates (-3, 3) to Polar Form
This article will guide you through the process of converting rectangular coordinates (-3, 3) to their equivalent polar form.
Understanding Rectangular and Polar Coordinates
- Rectangular Coordinates: A point is represented by its horizontal distance (x-coordinate) and vertical distance (y-coordinate) from the origin. This is the familiar Cartesian coordinate system.
- Polar Coordinates: A point is represented by its distance from the origin (radius, r) and the angle (theta, θ) it makes with the positive x-axis.
Formula for Conversion
To convert from rectangular coordinates (x, y) to polar coordinates (r, θ):
- Radius (r):
- r = √(x² + y²)
- Angle (θ):
- θ = arctan(y/x)
Applying the Formula to (-3, 3)
-
Calculate the radius (r):
- r = √((-3)² + (3)²)
- r = √(9 + 9)
- r = √18
- r = 3√2
-
Calculate the angle (θ):
- θ = arctan(3/-3)
- θ = arctan(-1)
Since (-3, 3) lies in the second quadrant, we need to adjust the angle. The arctan(-1) gives us -45°, but the angle in the second quadrant is 135°.
Therefore, the polar coordinates of (-3, 3) are (3√2, 135°).
Conclusion
By applying the formulas and understanding the relationship between rectangular and polar coordinates, we successfully converted the point (-3, 3) to its equivalent polar form (3√2, 135°).