Multiple Choice
Convert the point to rectangular coordinates.
15. Polar Equations
Convert Points Between Polar and Rectangular Coordinates
Multiple Choice
Convert the point to polar coordinates.
A
B
C
D
Verified step by step guidance1
To convert a point from Cartesian coordinates (x, y) to polar coordinates (r, θ), we use the formulas: r = √(x² + y²) and θ = arctan(y/x).
For the point (-2, 2), calculate the radius r using the formula: r = √((-2)² + 2²).
Simplify the expression for r: r = √(4 + 4) = √8 = 2√2.
Determine the angle θ using the formula: θ = arctan(2/(-2)). Since the point is in the second quadrant, adjust the angle to θ = π - arctan(1).
The angle arctan(1) is π/4, so θ = π - π/4 = 3π/4. Therefore, the polar coordinates are (2√2, 3π/4).
Related Videos
Related Practice
