User Name Remember Me? Password

 Calculus Calculus Math Forum

 August 6th, 2012, 08:09 AM #1 Member   Joined: Sep 2007 Posts: 77 Thanks: 0 Area of a Circle problem The area of a circle i. Let r be a positive real number and let O = (0, 0) and P = (r, 0) be points in the coordinate plane. Let ?? be the (half)-line that emanates from O and makes an angle ? with respect to the positive x-axis (see figure in attachment). Let Q be the point on ?? whose distance to O is r and let Q' be the point on ?? whose perpendicular projection onto the positive x-axis is P (see figure in attachment). Find the x and y coordinates of Q and Q'. ii. Partition the angle 2? into N equal parts of size ? and let Cr = area of a circle with radius r, A = area of the triangle ?OPQ, A' = area of the triangle ?OPQ', where O,P,Q,Q' are as in the above figure with angle ? = ?. (a) Show that A = r^2 sin(?) / 2 and A' = r^2 tan(?) / 2 (b) Explain why the inequalities Nr2 sin(?) / 2 ? Cr ? Nr2 tan(?)/ 2 hold for any r > 0 and any natural number N ? 3. (c) Find an expression for N in terms of ? and take the limit as ? --> 0 in (7) to find Cr. Can anyone help get me started on this? Thank you! August 6th, 2012, 10:15 AM #2 Math Team   Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Area of a Circle problem It is straightforoward that the x coordinate of Q' is simply r. Now, So, the y coordinate of Q' is Can you proceed for Q now? August 6th, 2012, 10:59 AM #3 Member   Joined: Sep 2007 Posts: 77 Thanks: 0 Re: Area of a Circle problem From there, I know that the coordinates of QP are (rcos x, rsinx). To find the area, I need to take the anti-derivative of the the function. However, even though we have the two coordinates, how do I know which formula to take the anti-derivative of? August 6th, 2012, 12:42 PM #4 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Area of a Circle problem 10.) i) We may use the definition of sine and cosine to find: Since we then find ii) a) Using the formula for the area of a triangle we then find: b) For any natural number and the geometrical interpretation of the given inequality is that for a circle of radius r, its area is greater than an inscribed N-gon and less than that of a circumscribed N-gon. c) and hence: August 6th, 2012, 12:47 PM #5 Member   Joined: Sep 2007 Posts: 77 Thanks: 0 Re: Area of a Circle problem Thank you for the help! As you can see from my prior post, I was really off from what I needed to do, so I appreciate the help in preparation for my final. Thank you thank you thank you! August 6th, 2012, 01:02 PM #6 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Area of a Circle problem To be more formal about the last part, we could state: Apply L'H�pital's rule to the limits (although this isn't necessary, just quicker): Tags area, circle, problem Search tags for this page

,

,

### let r be a positive real number and let o 􏰆 􏰎0, 0􏰐 and p 􏰆 􏰎r, 0􏰐 be points in the coordinate plane. let ℓθ be the (half )-line that emanates from o and makes an angle θ with respect to the positive x-axis (see ﬁgure). let q be

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post yeoky Algebra 4 May 3rd, 2014 01:06 AM Pivskid Algebra 11 July 3rd, 2013 08:25 AM nabilkud Algebra 1 October 20th, 2012 10:49 PM tiba Algebra 4 June 20th, 2012 11:45 AM gus Algebra 1 April 17th, 2011 04:25 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      