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The data for a polar plot is given in polar coordinates, which is given as R-theta, where R is the distance from the origin (center of the plot) and theta is the angle from a reference angle, such as north or conversely the positive horizontal axis of overlaid cartesian coordinates. A Polar Plot is not a native Excel chart type, but it can be. Therefore, we can use the Pythagorean theorem to find the length of the hypotenuse: r 2 = x 2 + y 2. r = x 2 + y 2. The angle θ can be found using the tangent function. Recall that the tangent of an angle is equal to the opposite side divided by the adjacent side. The opposite side is the y component and the adjacent side is the x component. 1. The second circle is in the upper-half plane. Also, the angle parametrizing the first circle ranged over π radians. Why would the second be any different? Actually, any interval of length π seems to work! The first circle can be parametrized as: r = 2 a cos θ and ϕ 0 ≤ θ < ϕ 0 + π, and the second as. r = 2 a sin θ and ϕ 0 ≤ θ.

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This is where I am stuck. I do not know how to write the $\mathbf{bounds}$ for this region (circle) in polar coordinates because the circle isn't centered at the origin. I tried converting the region equation to polar coordinates but that did not help and made the integration a huge mess. A hint would be much appreciated, I really want to solve.

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