21.Graph the following polar curves: a) r= 2+4 cos(0) b) r = 5 – 10 sin(0) For each of the graphs above, set up the integral(s) that calculates: the area of inner loop; • the area of outer loop; • the area between loops; • the arclength of the inner loop; • the arclength of the outer loop.

21.Graph the following polar curves: a) r= 2+4 cos(0) b) r = 5 – 10 sin(0) For each of the graphs above, set up the integral(s) that calculates: the area of inner loop; • the area of outer loop; • the area between loops; • the arclength of the inner loop; • the arclength of the outer loop.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 66RE

See similar textbooks

Similar questions

Find the exact length of the polar curve r=e2(theta) , where 0 is less than or equal too theta is less than or equal too ln(3).
1. The graph of the parametric curve x = cos^3θ, y = sin^3θ for 0 ≤θ ≤2πis a closed astroid of four vertices, centered at the origin. Sketch the graph and find the perimeter of the curve. 2. Find the area enclosed by the curve in problem 1.
6. Consider the curves: r = 2 + cos 2θ and r = 2 + sin 2θ, a) Sketch a graph of both curves on the polar graph provided. b) Find all points of intersection. c) Find the total area inside r = 2 + cos (2θ) and outside r = 2 + sin (2θ)
6. Consider the curves: r = 2 + cos2? and r = 2 + sin2?a) Sketch a graph of both curves on the polar graph provided.b) Find all points of intersection.c) Find the total area inside r = 2 + cos (2?) and outside r = 2 + sin (2?)
Which of the following is correct for the arclength of the polar curve
Find the area of the region inside one leaf of the polar graph: r = sin4x
Find the equation of the tangent line to the polar curve r = 3 + 8 sin θ at θ = π/6.Note that sin(π/6) = 1/2, cos(π/6) = √3/2.
Sketch the graph of the polar curve r = 1 + 3 sin θ and calculate the area it encloses.
1)Find the exact length of the polar curve r=2+2costheta
Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 9 + 4 cos(θ), θ = π/3
7. Given the polar curve r2 = cos 2θ, Find the points where the tangent lines are horizontal and vertical. Determine the equation of the tangent line at the point.... Use the graph provided to sketch a graph indicating the tangent lines.
Sketch r = 4 + 8 cos θ on the image below and find the area outside the inner loop of the curve using polar coordinates integration.