6. Consider the polar equation r = 2 – 2 cos(0) a) Complete the table of values for r = 2 -2 cos(0). |00 1 27 4 31 S 2n 3 2 3 3 2 3 b) Sketch the graph of r = 2 – 2 cos(8) using the points in part a).

Q: Q7:- sketch the graph of the following polar equation. 3- r = 6 cos 6 1- 0 = 6. 5- r= 3(1- sin0) 2-…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 3. Draw the polar curve r = 1+3 cos 30

A: THE POLAR CURVE OF THE GIVEN FUNCTION r=1+3cos3x will be,

Q: 24. Which of the following polar curves is a cardioid? A. r= cos () B. r= 2+3sin® C. r = 3– 20ose…

A: 24)      A. r=cos2θ2                                                         B)r=2+3sinθ…

Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E¹r = g(0) = 1/250c4 SOC 3 D:r=3 (1.)…

A: As per the question we are given two curves in polar coordinates as : C : r = f(θ) = 3 - 3cos(θ) E :…

Q: 2. 6 27 4 6 2 Find three additional polar representations of the point, using -2n < 0 < 2n. (Enter…

A:

Q: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

Q: Graph the family of polar equations r = 1 + c sin 2u for c = 0.3, 0.6, 1, 1.5, and 2. How does the…

A:

Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

A:

Q: Consider the polar curves C₁ : r = 2 cos 0 and C2 : r = 2 cos 30, and let R be the shaded region as…

A: Given: C1:r=2cosθC2:r=2cos3θ To find: Area of the region

Q: Use a graphing utility to graph the polar equation. Between the loops of r = 3(1 + 2 sin(0)) 4 6 4 0…

A:

Q: Write a polar equation for the conic with the given characteristics. e = 1.6; directrix: y = 4 6.4…

A: Given :  Eccentricity,   e=1.6       and  Directrix,         y=4

Q: Draw the polar curve r = cos(30) with its orientation. Set up all integral to evaluate the length of…

A: First, find the node to the polar curve by equating r = 0, so cos(3θ)=rcos(3θ)=0(3θ)=-π2,π2θ=-π6,π6…

Q: Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the…

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Q: Sketch a graph of the polar equation. r- -2(1 + sin(0)) n/2 7/2 4. 2 .4 4 -2 2 4. -2 -4 n/2 7/2 4. 4…

A: Given, r= -2(1+ sin theta) Plotting for the given polar coordinates we have,

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: Given: polar curves C₁ : r = √2- cos 0 and C₂ : r = √2+ sin intersecting at A(³√2, 37) and B(2,7) 2…

A:

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of e…

A:

Q: Find the area of the inner loop of the limaçon with polar equation r = 2 cos 0 – 1 (Figure 21). -1…

A:

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

A:

Q: Given the polar curves: C₁:r = 2 cos 0 ग 2 A(2,0) C2 B(0,0) C₂:r = 2 cos 30 0 The two curves…

A: Any point in the Cartesian coordinate system is represented by the ordered pair x, y. Any point in…

Q: Graph the equations in Exercises 17–24 in the θr-plane. Label each arc of your curve with the…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 1. Change ſ, Lz xy dydx to polar form. 4-x2

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: 1. The polar equation of the graph whose equation is x² + y2 = 25 is (A) r- 5cos 0 = 0 (B) r+5cos 0…

A:

Q: 3) Sketch the polar curve r = 1 + 2 cos 0. In your graph, label the points corresponding to the…

A: See the attachment

Q: Part A, B, and C

A: According to the given information it is required to sketch the graph of the given polar equation.…

Q: 4. Find the exact length of the polar 2 cos os 0, 0 < 0 < T. curve r

A: Given: r=2cosθ on 0,π L=Length of Polar curve= ∫ab(r(θ))2+(r'(θ))2dθ now, r'(θ)=ddθ(2cosθ)=-2sinθ…

Q: Find dy/dr and the slopes of the tang ent lines shown on the graph of the polar equation r = 2+3 sin…

A: According to question, r = 2 + 3 sin θ

Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: 4. Sketch a clear and accurate graph of the polar equation r 1-2cos 0.

A: To sketch a clear and accurate graph of the polar equation r=1-2cosθ Here r is the distance from the…

Q: 7) Find the points at which the polar curve r = 1+ cos® have horizontal or vertical tangent lines.

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Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

A:

Q: Consider the polar curves C₁ r = 2 cos 0 and C₂: r = 2 cos 30, and let R be the shaded region as…

A: Same point can be expressed in polar coordinates in various ways.

Q: Consider the graph of a polar curve in the r0-plane plotted only from 0 = 0 to 0 = 27/3. Plot this…

A:

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

A:

Q: 8. the same graph as the polar equation r-6cos0 =0 and graph on the xy plane. Find an equation in x…

A: The given polar equation is r-6cosθ=0 The equation in x and y is to be calculated and graphed in the…

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: 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: 6. Find the length of the polar curve r = 1+ cos 0 on the interval 0 < 0 < n.

A: Given:

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

A:

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

A: The value of the cosine function  cos0=1cosπ6=32cosπ4=12cosπ3=12cosπ2=0cosπ=-1cos3π=-1cos2π=1

Q: 1. Sketch the graph of r=1-cos in polar coordinates. [3 marks]

A:

Q: . Show that the equations x = r cos 0, y = r sin 0 transform the polar equation 1 + e cos 0 into the…

A:

Q: Give an example of two polar equations, r1(0) and r2(0), whose graphs intersect in at least two…

A: According to the given information, it is required to give an example of two polar equation whose…

Q: 6. Consider the polar curves C1 and C2 described by the polar equations r = 2 – V2 sin(0) and r = 1,…

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Q: 4. Draw the polar curve defined by r= 3 –2 cos 30.

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Q: b. Plot the polar curve r= 2(1- cos0) in interval t ,2n

A: Given equation is r=2(1-cosθ)  =2-2cosθ

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

A: Given: r=3+5 cosθ We have to sketch the graph of r as a function of θ in Cartesian coordinates…

Q: 3.3. Show that in a polar coordinate system, the distance d between the points (r1,01) and (r2, 02)…

A: The distance between r1,θ1 and  r2,θ2 is d=r12+r22-2r1r2cos θ1-θ2

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