While you may have gotten the correct answer, if you plot that circle you will see that the appropriate interval of integration would be ##[-\frac \pi 2,\frac \pi 2]##, not ##[0,\pi]##.Malabeh said:EDIT: I don't know how to delete a post but I got it. My calculator was in degree mode.
It works both ways, does it not?LCKurtz said:While you may have gotten the correct answer, if you plot that circle you will see that the appropriate interval of integration would be ##[-\frac \pi 2,\frac \pi 2]##, not ##[0,\pi]##.
The formula for finding the area of a circle in polar coordinates is A = (1/2)r^2θ, where r is the radius of the circle and θ is the central angle in radians.
To convert rectangular coordinates (x, y) to polar coordinates (r, θ), you can use the formulas r = √(x^2 + y^2) and θ = tan^-1(y/x).
No, the Pythagorean theorem cannot be used to find the area of a circle in polar coordinates. It can only be used for finding the distance between two points in a Cartesian coordinate system.
To find the area of a sector in polar coordinates, you can use the formula A = (1/2)r^2θ, where r is the radius of the circle and θ is the central angle in radians. This formula is the same as finding the area of a circle, but you must first convert the central angle from degrees to radians.
No, both r and θ must be positive values in order to find the area of a circle in polar coordinates. Negative values would result in imaginary or undefined solutions.