A show that the polar equation of this curve has the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: encloses. 37. r = 2 + cos θ . 38. r = 2 cos 3θ . These approximations improve as the triangle narrows. θ =β y c In Exercises 39 and 40, use a graphing utility to drawn the polar curves. Then use a CAS to find the area of the region inside the first curve and outside the second curve. 39. r = 4 cos 3θ , r = 2. 40. r = 2 cos θ , r = 1 − cos θ . c 41. The curve whose equation in rectangular coordinates is x ρ (θ ) y θ Ω x r = ρ (θ ) y2 = x2 a−x , a+x a > 0, is called a strophoid. (a) Show that the polar equation of this curve has the form r = a cos 2θ sec θ . (b) Use a graphing utility to draw the graph of the curves for a = 1, 2, and 4. (c) Let a = 2. Find the area inside the loop. θ =α 33. Following the approach used in Section 6.4, show that the rectangular coordinates of the centroid of are given by xA = 1 3 β α [ρ (θ )]3 cos θ d θ , . yA = 1 3 β α c 42. The curve whose equation in rectangular coordinates is [ρ (θ )]3 sin θ d θ (x2 + y2 )2 = ax2 y, a > 0, where A is the area of is called a bifolium. (a) Show that the polar equation of this curve has the form r = a sin θ cos2 θ . (b) Use a graphing utility to draw the graph of the curves for a = 1, 2 and 4. (c) Let a = 2. Find the area inside one of the loops. In Exercises 34–36, use the result of E...
View Full Document

This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

Ask a homework question - tutors are online