This is not a graded question despite the due date -- it is supplemental work to help us learn the lecture material (my teacher just gave an assignment she was using for another class).My question is #7 -- Show that y=2asin^2(theta)Thanks in advance,Gabriel Sheets Due 3/1/2021 at 11 anm2) Shaw thet d= stneStn 6 =to스3) Shan that x=Zacotosine(Notes x=d cos Đ.至)Cos e =tan eza%3Dtane%3Dzax-= 2a cotevtane4 What is neetsake home Quiz 1 - Due 3/1/2021 at 11 amThe Witch of AgnesiMany plane curves in mathematics are named after the people who first investigated them, like the folium of Descartesor the spiral of Archimedes, However, perhaps the strangest name for a curve is the witch of Agnesi. Why a witch?Maria Gaetana Agnesi (1718–1799) was one of the few recognized women mathematicians of eighteenth-century Italy.She wrote a popular book on analytic geometry, published in 1748, which included an interesting curve that had beenstudied by Fermat in 1630. The mathematician Guido Grandi showed in 1703 how to construct this curve, which helater called the "versoria," a Latin term for a rope used in sailing. Agnesi used the Italian term for this rope, "versiera,"but in Latin, this same word means a "female goblin." When Agnesi's book was translated into English in 1801, thetranslator used the term "witch" for the curve, instead of rope. The name “witch of Agnesi" has stuck ever since.The witch of Agnesi is a curve defined as follows: Start with a circle of radius a so that the points (0, 0) and (0, 2a)are points on the circle (Figure 1.12). Let O denote the origin. Choose any other point A on the circle, and draw thesecant line OA. Let B denote the point at which the line OA intersects the horizontal line through (0, 2a). The verticalline through B intersects the horizontal line through A at the point P. As the point A varies, the path that the point Ptravels is the witch of Agnesi curve for the given circle.Witch of Agnesi curves have applications in physics, including modeling water waves and distributions of spectrallines. In probability theory, the curve describes the probability density function of the Cauchy distribution. In thisproject you will parameterize these curves.(0, 2а)elxiy)Figure 1.12 As the point A moves around the circle, the point P traces out the witch ofAgnesi curve for the given circle.1. On the figure, label the following points, lengths, and angle:a. Cis the point on the x-axis with the same x-coordinate as A.b. x is the x-coordinate of P, and y is the y-coordinate of P.C.E is the point (0, a).d. Fis the point on the line segment OA such that the line segment EF is perpendicular to the line segmentOA.e. bis the distance from O to F.f. cis the distance from F to A.g. dis the distance from O to B.h. 0 is the measure of angle 2COA.1

Name: This is not a graded question despite the due date -- it is supplement
Uploaded: 2024-03-20T06:46:55.000Z
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Description: This is not a graded question despite the due date -- it is supplemental work to help us learn the lecture material (my teacher just gave an assignment she was using for another class).My question is #7 -- Show that y=2asin^2(theta)Thanks in advance,