Please solve question two and show steps Problem statement Suppose that T is the

Question

Please solve question two and show steps Problem statement Suppose that T is the triangular region shown with vertices at (0,0), (0,1), and (1,1). Describe T using polar coordinates. Compute the area of T using integration in polar coordinates. Problem statement A window is in the shape of a 2' by 3' rectangle surmounted by a semicircle. Describe the boundary of the window as r = f(theta) in a polar coordinate system whose location and orientation you specify. The f(theta) likely will need to be defined "piecewise". Comment A calculus course traditionally has a problem concerning this sort of window, including the rather uncommon word "surmount" as part of the description. Tradition is honored here!

Explanation / Answer

solution -: since we are given 2 ' by 3'

the point (0,0) should be (1, 2) so that it is halfway between since we have a 2 by 3 and a semicircle..

Now, The centre point of the coordinate axes should be such that f(theta) = 1.5

the line x = -1.5 is the line -1.5 = r cos(theta)

the line x = 1.5 is 1.5 = r cos(theta)

if (0,0) is the bottom left corner of the window in cartesian coordinates, then the point (1.5, 2) is the point (0,0) in the new coordinate system.   Answer

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