(c) Find z,z, in polar form given z, =5/3cis(120) and z, =V2cis(210).

Q: Q17:- In polar coordinates prove that** 第。

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Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.

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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: (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 an equation in x and y that has the same graph as the polar equation r- sin 0 = 0 and graph on…

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

A: We need to find the length of the polar curve

Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: Find the exact length of the polar curve r=1+ cos 0

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Q: Find a polar equation in the form r cos (θ - θ0) = r0 for each of thelines y = -5

A: We need to find the equation in polar form for the given line

Q: Find the angle α between the polar curves r1=eθ and r2=e−θ at the point of intersection.

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

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Q: 9. Find other polar coordinates (r,) of the point in polar form given by (3,) for which r <0 and -2π…

A: answer is in next step . please give a like!!

Q: Find the exact length of the polar curve. = 02, 02, os 0s 2A

A: Given polar curve is and

Q: 3 4. Sketch the region described in polar coordinates by r < Cos e

A: We need to sketch the region.

Q: Find the area of the region enclosed by one loop of the curve for the polar equation r = 2sin3θ.

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Q: (). 3 Calculate the length of the polar curve r = 8 sin' 3 in the interval 0 < 0<.

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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: Find the exact length of the polar curve. 4 sin(0), o 0S T/3

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Q: Find the exact length of the polar curve. r = 3 sin(0), 0≤0 ≤ π/4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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

A: In the given question we have to find the length of the polar curve on the interval . Concept:…

Q: 9. Sketch the polar curve. r = 2 cos 2 0

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Q: 5. Consider the point with rectangular coordinates (1, – V3 ). sState the coordinates of the point…

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Q: 9. Sketch the polar curves r = 5sine and r = 5 sin(30) on the same grid below.

A: The given polar curves are  r=5sin(θ)r=5sin(3θ)

Q: Find an equation in x and y that has the same graph as the polar equation r-sin 0 =0 and graph on…

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Q: Find the slope of the polar curve at the indicated point. r -6+5 COs o 2.

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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: 9. Sketch the polar curve.r= 2 cos 2 0 ||

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Q: Q2 Find the points of intersection of the polar curves r=1+cos 9 and r= -cos

A: Point of intersection of the Polar curve

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: Prove that the distance, d, between two points with polar coordinates (r, 01) and (r2, 02) is d =…

A: Distance (d) between two points x1, y1 and x2, y2 is  d=x1-x22+y1-y22   ....1

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: 3. Graph the polar equation and find the area of the region. Between the loops of r = 2 – 6 cos 0

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Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

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Q: compute the length of the polar curve. r =√1 + sin 2θ for 0 ≤ θ ≤ π/4

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Q: 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: A tangent at the pole to the polar curve r = V2 - 2 cos 0 is 0 = A

A: A tangent at the pole to the polar curve r=2-2 cos θ is, for the tangent at the pole we have,…

Q: Find an equation in x and y that has the same graph as the polar equation r-sin e =0 and graph on…

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Q: 2) Sketch the graph of the curve with the polar equation: r= 2– sin(20).

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Q: Which of the following shows the correct sketch of the polar curve r = 9 sin(3 0)? 10 -10 5 10 -5…

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Q: Consider the polar curve r=2sin(30) for 0s0sn.

A: Given polar curve is r=2sin3θ for 0≤θ≤πfind the area of the region inside the curve

Q: compute the length of the polar curve. r = cos2 θ

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Q: Find the exact length of the polar curve r=3sin(θ),0≤θ≤π/3

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

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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: Q2 Find the points of intersection of the polar curves r=1+cos and r= -cos

A: Given polar curves are  r=1+cos θ r=-cos θ Find the points of intersection. At first, the value of θ…

Q: What is the exact length of the polar curve 1 = 3 cos 0, 0 O<T?

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Q: Find the length of the polar curve r = 5°; 0 <e< 2n

A: Given ,r=5θdifferentiate w.r.t.θdrdθ=5θ.ln(5)Weknow that length of the curve…

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