55. DISCUSS - DISCOVER: A Transformation of Polar GraphsHow are the graphs ofr = 1+ sin e6.andr = 1+ sin 0 -related to the graph of r = 1 + sin 0? In general, how is thegraph of r = f(6 - a) related to the graph of r = f(0)?

The graph of the polar curve r=1+sinθ-π6 can be obtained by rotating the graph of r=1+sinθ in…

Answered: 55. DISCUSS - DISCOVER: A…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.2: Graphs Of Polar Equations

Problem 65E

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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)
5. Find the area of the region that lies inside the curve whose polar equation is r = 3 sin θ andoutside the curve whose polar equation is r = 2 −sin θ. (Hint: First, sketch the two curves onthe same axes and shade the region of interest.)
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?)
Use a graphing utility to graph the polar equation. Between the loops of r = 5(1 + 2 sin(θ)) How would you figure this out and get the graph?
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.
Consider the graph given in polar coordinates by r=2cos(4@) a)sketch the graph of r(@) when @ is greater than or equal to 0 and less than or equal to pi/4. b) What is the area enclosed by the graph when @ is greater than or equal to 0 and less than or equal to pi/4? c)How do you use this to calculate the area enclosed by the graph when @ is geater than or equal to 0 and less than or equal to 2pi.?
Use a graphing utility to graph the polar equation. Find the area of the given region analytically. Inner loop of r = 4 + 8 sin θ
Use a graphing utility to graph the polar equation r = (3π/2) sin 3θ . Find an interval for over which the graph is traced only once
Use a graphing utility to graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve. r = 2 sin(2 cos θ), [0, π]
Find the smallest interval for θ starting with θ min = 0 so that your graphing utility graphs the given polar equation r = 4 sin 2θ exactly once without retracing any portion of it.
a) Use Polar-style integration to find the area contained within one petal of the Polar rose with equation r=5sin8theta.For convenience, use the First petal fully graphed on the interval [0, 2Pi]. b) When graphed over the [0, 2Pi] interval, how many petals does r=5sin8theta have in its’ graph? How much area, total, do they contain? (use your a) answer to help get this one) c) The Polar Rose in a) and b) above is bounded (encircled!) by the graph of the circle r = 5. What is the area of the region that is Inside this circle but Outside of the Rose? (don’t integrate to get this answer, there’s no need – use b)'s answer to help get it)
Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ as shown in the figure on the right. The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. Let P be the point of intersection of C1 and C2 in the second quadrant. Find polar coordinates (r, θ) for the point P where r > 0 and θ ∈ [0, 2π].

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55. DISCUSS - DISCOVER: A Transformation of Polar Graphs How are the graphs of r = 1+ sin e 6. and r = 1+ sin 0 - related to the graph of r = 1 + sin 0? In general, how is the graph of r = f(6 - a) related to the graph of r = f(0)?