Task 2: Analyze the graphs of the polar equations r= acos(n8) and r= asin(n®) when n is an even integer. a. What is the maximum value of r? b. Sketch the graphs when n = 2 c. Sketch the graphs when n = 4

Q: CONVERT the below graph in the xy-plane TO a graph in the polar plane FOR ONLY the interval A/2 2' 2…

A: TO convert a graph from xy plane to polar plane we need to find points on the graph  from the xy…

Q: Sketch the polar graph of r=3

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Q: Task 2: Analyze the graphs of the polar equations r= acos(ne) and r= asin(ne) when n is an even…

A: Solution: Part (a)     The maximum value of r is a.   Part (b) sketch the graph when n = 2

Q: (b) Use appropriate software to sketch the following polar curves i) r = cos(7.10) + cos² (0) ii) =…

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

Q: Find the exact length of the polar curve described by: 9e -0 on the interval

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Q: r = 5°, 0<0<2n

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Q: find the exact length of the polar curve r = θ2,    0 ≤ θ ≤ 2π

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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…

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Q: How many times do the graphs of the polar curves r=3 and θ=π/6 intersect?

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Q: Determine the shape of each polar curve. 9r = 7 parabola 7 circle 9 r = 4 + 6 sin(0) ellipse…

A: Given :            r=7r=74+6sinθr=74+4sinθr=76+4sinθ

Q: Task 2: Analyze the graphs of the polar equations r = acos(ne) and r = asin(ne) when n is an even…

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

A: r=2(1-cosθ) in the interval π , 2π

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. Let r(0) = 2sin(0) + cos(Ⓒ) be the polar definition of a planar curve. Find, in standard x-y…

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Q: Find the exact length of the polar curve r=e2(theta) , where 0 is less than or equal too theta is…

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Q: Graph the polar curve r = 2+4 cos 0

A: To graph the given polar curve Given polar curve is r = 2+4cosθ

Q: Find the exact length of the polar curve described by: r = 8e 3 on the interval a <o< 9n. 2"

A: The length of a polar curve r=fθ in the interval α≤θ≤β is given by L=∫αβfθ2+f'θ2dθ. The given curve…

Q: Find the exact length of the polar curve. r = e80, 0 < 0 < 2n

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Q: Graph the line and conic section. r = 8/(4 + cos u)

A: Graph the line and conic section. r = 8/(4 + cos u)

Q: Find the exact length of the polar curve described by: r = 5e-0 %3D 7 on the interval

A: The given function is r=5e-θ, where  7π2≤θ≤6π. The length of the polar curve is obtained by the…

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: Match the graph with its polar equation. r = 3 (1 + cos(0)) T/2 1/2 4| -2 2 4 -2 -2 л/2 T/2 3- 2 1…

A: Topic :- Geometry As per our guidelines , In case of multiple different questios ,at a time only one…

Q: Consider the curves: r = 4sin 0 and r = 2 sin(0) + 2cos (8). a) Sketch a graph of both curves on the…

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Q: Sketch the graph of the polar equation.r2 = 4 cos 2θ (lemniscate)

A: The polar equation is,r2=4 cos 2θ

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: 16) (10.) Find three ordered pairs (r, 0) on r = 2cos(30) and sketch the graph of the polar…

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

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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: 5. Sketch the graph of r=-6sin 8 M t WY COMP He ww 4 (8.4 16, 17) 2² IN Challenge problem: Write the…

A: 5) a) To Sketch: Graph of r=-6sinθ. (b) To Find: Polar equation of the graph shown in the figure.

Q: Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos 6 in polar ㅠ 즈 2m 3m 5л…

A: Graph Tracing and polar curve.

Q: 1. Sketch the graph of r = 2 sin(20) in polar coordinate system T/4 31/4 5T/4 7T/4 in the polar…

A: Consider the provided polar equation, Sketch the graph of the polar equation. Now make the graph of…

Q: Consider the rose curve with polar equation r = cos(20), whose graph is shown below. 0.5 -0.8-0.4서…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

Q: 6. Consider the polar equation r = 2 – 2 cos(0) a) Complete the table of values for r = 2 -2 cos(0).…

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Q: The figure above shows the graphs of the polar curves r = 2 cos (30) and r = 2. What is the sum of…

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Q: Find the exact length of the polar curve. r- e88, ose s 2n

A: The arc length of a polar curve r = f(θ) between θ=a and θ=b is given by the integral L=∫abr2+drdθ2…

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: (b) Sketch the graph of the following polar curves 0 = n/4, for all r. Find it's equivalent forms in…

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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: Sketch the graph of the polar equation.r = e2θ, θ ≥ 0 (logarithmic spiral)

A: Consider the given polar curve to be r=e2θ, θ≥0.

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: 11 write the rectanqular coordinate equation x2+y²= coordmates and sleetch the graph, in polarr

A: Given the equation x2 + y2 = x in the rectangular coordinates and we have to convert into polar…

Q: 1. Consider the equations r = 8cos 30 and r=4. a. Find all points of intersection of the two curves.…

A: The equation of the curve is The equation of the curve is r = 4

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: While playing at the Nawaka Sevens, four of the rugby players are observed to be located at the…

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: Sketch a graph of the polar equation r2 = 4 cos 2

A: Given:       r2=4 cos2θ First, notice that             r2=4 cos2θ⇒4 cos2θ=2cos2θ Applying following…

Q: For what value of k does the polar graph r= ksine + 1 produce a horizontal tangent at 9-? Ok= 1…

A: We will solve the problem

Q: Find the exact length of the polar curve described by: r = 7e-0 3 on the interval 10

A: r=7e-θ,    310π≤θ≤6π Differentiating with respect to θ, we get drdθ=7-e-θ=-7e-θ