Q1: Find the polar coordinates of the Cartisian point P(-5,5) Q2: Express the function In r = In(cot 0) + In (csc 0) by cartesian form

Q: Q2 Q1 Find the points of intersection of the polar curves r-cos () = 0 and 2-cos A-r=0

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Q: The polar curver is = sin' 1. Onot symmetricabout the x-axis Osymmetric about the x-axis 2. Onot…

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Q: Q2 Q1 Find the points of intersection of the polar curves r-cos 0 = 0 and 2-cos-r=0

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Q: Find the points of horizontal tangency to the polar curve. r = a sin θ      0 ≤ θ < π, a > 0…

A: Calculation:The polar curve is r = a sin θ, where 0 ≤ θ < π and a > 0.In order to find the…

Q: II. Given the polar curves 62 r = 1 + sin and : 63 r = 3 sin 0. 1. Determine the intersection points…

A: Let us consider the curve r=f(θ), θ1≤θ≤θ2 The area under the curve is obtained as, Area=12∫θ1θ2r2dθ…

Q: 1. Let C be the polar curve given by r = 2+ sin 0, –T/4<0 <#/2. Sketch the curve. b. Indicate with…

A: Given : C: polar curve=r=2+sin θ,      -π4≤ θ≤π2 (a)   The  graph of the polar curve and  (b)…

Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan…

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Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

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Q: compute the length of the polar curve. The length of r = θ2 for 0 ≤ θ ≤ π

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Q: Q1 Find the points of intersection of the polar curves rcos and 2-cos-r=0 Q2 Find the points of…

A: Introduction: The polar curve has the form r=fθ. When two polar curves intersect each other, the…

Q: 3. Sketch the polar curve r = 2 sin 30 by first sketching the graph of r as a function of e in…

A: Given the polar curve, r=2 sin3θ                ...(1)

Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

A: To solve the following problem

Q: Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that…

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Q: In polar coordinates, a polar function exists by the name of strophoid, with equation r = sec 0 – 2…

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Q: 1) For the point with polar coordinates 9. determine three different sets of 7 Зл coordinates for…

A: We have to write same polar coodinate (r,theta) in different ways:

Q: 13) Find as all polar points (r, 0) of horizontal and vertical tangency to the curve: x = cos(20) y…

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Q: Q1) A) Replace the polar equation r? sin 20 = 2 by equivalent Cartesian equation. B; C) Find the…

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Q: 6. Consider the curves: r = 2 + cos 2θ and r = 2 + sin 2θ, a) Sketch a graph of both curves on the…

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Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

A: We equate the two equation to find solutions.

Q: 2. Consider the polar curves C,:r= 8cos(20) and Ca:r = 4v2 Cir=4V2 Cir=8 cos(20) 10 12 14 10 a. Find…

A: The polar curves are given as , C1:r=8cos2θ and C2:r=42

Q: 12. (a) Sketch the curve in the polar coordinate system with directions, (b) Find the values o for…

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Q: The slope of the tangent to the polar curve r 2 sin(0) at 0 = is O- V3 None of these 1 V3 V3 1 V3…

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Q: Consider the polar curves C1 : r = 3 – 2 sin 0 and C2 : r = 4sin 0. Let A and B be the points of…

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Q: O Sketch the polar curves r=4-4sin@ and r=8sin(-Ø) on one graph. Hence, determine the points of…

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Q: 4) The Cartesian coordinates for a point are (-1,-V3). Find polar co- ordinates (r, 6) for the point…

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Q: Q1 Find the polar coordinates of the Cartesian point (1,1) Q2 Express the function r = 4 tan 0 sec 0…

A: Since you have posted multiple question..so I have to give you the solution of first two only…

Q: For the polar equations r1=1-cosx and r2=1, (1)sketch the graphs of r1 and r2 in the same coordinate…

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Q: 14) (a) Given the polar equation r = 1 - 2sin(e), sketch the curve by first sketching the graph of…

A: the red line represents the cardioid r=1-2sinθ and the blue line represents the x2+y2=x2+y2-2y where…

Q: Consider the polar curves r = 3 and r = 3 + cos 3θ. Both curves are symmetric about the polar axis.…

A: We have to set up the integral for the given region.

Q: √2 2. Consider the polar curves C₁:r = 4 + ³√² cos 0 and C₂: r = 2 - ² cos € as shown in the figure…

A: b. Consider the given polar curves, C1:r=4+322cosθ and C2:r=2-222cosθ the diagram is shown below,…

Q: 9/3 9. to polar coordinates. Enter exact values Convert the point with Cartesian coordinates - for r…

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Q: 6. a) On polar graph paper, sketch the cuve given by r = 2 sin(0). b) Find 2 and explain how you…

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Q: Find the points of horizontal and vertical tangency (if any) to the polar curve. (Order your answers…

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Q: Calculate the length of the polar curve r =1-sin Oon the given interval (0, 2).

A: Formula to find the arc length helps to find the required arc length. Formula to find the arc…

Q: 6 Find three additional polar representations of the point, using -2n < 0 < 2n. (Enter your answers…

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Q: Find the slope of the polar curve at the indicated point. r = 1 - sin θ, θ = pi/4 a) square…

A: Topic - slope of a polar curve

Q: Find the length L of the polar curve r = 6 sin for 0 < 0 <- 2 2 OL= 12 OL= 6 OL = 6/2 OL = 12 – 6/2

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Q: Sketch the polar curves r= 9 sin 0 and r 4-9 sin 0. Indicate the co- ordinates of all r and y…

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Q: 10. Consider the curve with polar equation r = 6 sin 0 where 0< 0 <T. WVithout finding the Cartesian…

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Q: 8 sin ( *(4) in the interval 0 < 0< . Calculate the length of the polar curve r =

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Q: (iii) 3rd subplot is A butterfly curve using polar coordinates: 2a - I r = esina – cos(4a) - sin( 24…

A: (iii) Matlab Code: clc; clear all; close all; theta= 0 : pi/32 : 8 * pi; r= e.^…

Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

Q: 11 Final the directrix of the polar curve r = 9-2 cos 0 11 99 x = 2 99 2 0 x = - 11 x = -

A: To find- directrix

Q: Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that…

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Q: Both the polar curves r 3-2cose and r=-3+2 cos0 are symmetric to what axis O Line OX or the polar…

A: To find the symmetry of both the curves, r=3-2cos θ and r=-3+2cos θ, plot the graphs of both the…

Q: The graph of the polar equation r(0) = 0 cos(0), o ses. with derivative = cos(e) – 0 sin(0), is…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The polar equation of the curve is expressed as r = 2sine + 2cos0. Compute the area bounded by the…

A: The polar equation r=2sinθ+2cosθ represents a circle in the interval 0≤θ≤π. Beyond this interval the…

Q: 7) Sketch the polar curve r = 2(1+ sin 0). In your graph, label the points corresponding to the…

A: We have to find out the graph and points according to value of θ

Q: Graph the polar curve given by the equation below and plot/label the values of 0 = 0, T/2, T and…

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