In Exercises 40–46, convert each polar equation to a rectangular equation. Then use your knowledge of the rectangular equation to graph the polar equation in a polar coordinate system. 37 41. 0 = 4 40. r = 3 42. r cos 0 = -1 43. r = 5 csc 0 45. 4r cos 0 + r sin 0 = 8 44. r = 3 cos 0 46. r sin 20 = -2 %3D

Q: 2. Convert the polar equation to rectangular coordinates. 1 r = 1+ sin 0

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Q: 4- The equivalent of Cartesian equation (x + = 1) in polar equationis:

A: Given: Cartesian equation:   To determine: equivalent polar equation.

Q: Find two polar coordinate representations for the rectangular coordinate point (-√2, √6), one with…

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Q: 5. Convert the polar equation to a rectangular equation. r = -2 sin 0

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Q: 12/2 Use polar coordinates to evaluate dydx.

A: The region is bounded by x=1,x=2,y=0 and y=x

Q: Consider the conic section given by the polar equation 4 1-sin 0 r=

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Q: 24/ Replace the polar equation r. sin (0 +") = 2 to Cartesian equation -(G+ ns./ = 2

A: The given polar equation is r·sinθ+π6=2 .................(1)

Q: For each point (x,y), give two sets of polar coordinates, where 0<=theta<=2pi problem : (3√3,-3)

A: Polar coordinates.

Q: Determine whether the statement " If x &gt; 0, then the point (x, y) on the rectangular coordinate…

A: Consider a point (x, y) on the rectangular coordinate system  Draw a line joining that point to the…

Q: Sketch the graph of polar equation.Be sure to test for symmetry. r = 3 sin θ

A: Solution:Given          r= 3 sin θTo sketch the graph of polar equation test for symmetry

Q: Question in Image.

A: To convert to polar form replace:  x with r cos θ y with r sin θ   We have y = 7x + 12   r sin θ =…

Q: Given polar equation is r = 2- cos 0

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Q: Transform the equation r = 6 cos θ from polar coordinates to rectangular coordinates

A: The formulae shown below shows the relationship between polar coordinates and rectangular…

Q: The simplest method of graphing a polar equation is to plot points by substitutingconvenient values…

A: The simplest method of graphing a polar equation is to plot points by substitutingconvenient values…

Q: Convert the point with Cartesian coordinates 2 r and 0, with r> 0 and 0 ≤ 0 < 2π in radians. (r, 0)…

A: Topic = Geometry

Q: Convert the polar equation to a rectangular equation. 2 sin 20 = 4 %3D

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Q: What are the polar equations of the lines parallel to the line r cos (0 - ) = 1?

A: As a first step we will convert the polar equation into the Cartesian equation.

Q: Convert the Polar equation to a Cartesian equation and solve for y. r2 sin(0) cos(0) +r cos(0) = 2

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Q: 1/A) Replace the polar equation by equivalent Cartesian equation r2cose + 2sino

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Q: Replace the polar equation with an equivalent Cartesian equation. r 2 + 2r 2 sin θ cos θ = 576…

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Q: Convert the polar equation to rectangular form 9r cos 0 + 2r sin 0 = 1

A: We will convert the polar equation into rectangular form as following.

Q: 23) (Section 9.1/9.2) Convert polar equation r =3sin O to a rectangular equation

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Q: Determine the points at which the limacon defined by the polar equation r = 3+ 2 sin 0 has…

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Q: What are the polar equations of the lines parallel to the liner cos (θ − π/3)= 1?

A: rcosθ-π3=1

Q: 5/3 Convert the point with Cartesian coordinates 2 to polar coordinates. Enter exact values for r…

A: Convert the point with Cartesian coordinates 52,-532 to polar coordinates.Enter exact values for r…

Q: 4 Convert the equation from polar to cartesian. r = 3 – 2 sin 0

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Q: 2. Transform the polar equation into a Cartesian equation. 4 r = 4 + sin 0

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Q: Replace the polar equation r. sin (0+ 1 (0+²) = 2 to Cartesian equation

A: See the details solution in below

Q: 1. Convert Rectangular Equation to Polar Equation. x² = 9 – y?

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Q: In Exercises 59-74, convert each polar equation to a rectangular equation. Then use a rectangular…

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

Q: Consider the polar equation defined by r= 5 cos(2 sin 6), where 0<0< 2x. Determine the missing…

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Q: Replace the Cartesian equation with an equivalent polar equation. x2-y2=4 O cos2e - sin20 = 4 O r…

A: 1. x2-y2=42. r2=26r cosθ-6r sinθ-9

Q: / 2-Replace the Cartesian equations with equivalent polar equations. 1]. x-y? =1

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Q: 2. The point (4,30°) in plane polar coordinates is equivalent to .. in rectangular coordinates. (a)…

A: Given polar coordinates is  (4,30°)

Q: QI-Replace (x-2) y-4 to equivalent polar coordinate and sketch ir?

A: Since you have posted multiple question in this question which are not interlinked so I have solved…

Q: Given polar equation is r= 1- cos 0

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Q: Replace the polar equation with an equivalent Cartesian equation.  7r cos θ + 9r sin θ = 1

A: Answer is mentioned below

Q: Express the polar equation r=2 sin 0 in cartesian coordirates.

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Q: 1 r = sin 0-4 cos 0

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Q: Convert the Cartesian equation y = x2 + 2x into a polar equation (you should be able to simplify…

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Q: Sketch the curve with the given polar equation, and find its Cartesian equation. 2 =-4 sin 20 %3D y

A: We are given the polar equation . Let us plot the figure.

Q: 2. Convert Polar Equation to Rectangular Equation. 1 r = sin 0 – cos 0

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Q: Convert the polar equation to rectangular form. 8 r = 1 - cos 0

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Q: 10 Write an equivalent rectangular equation for the polar equation r = 3 sin 0-7 cos 0

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Q: Convert the rectangular equation 2x - 4y = 5 into polar form. 1 O r = 2 cos 0-4 sin 0 5 Or 2 sin 0-4…

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Q: Convert the polar equation to rectangular form. r = 1 - cos 6

A: Find rectangular form

Q: 5 Convert the equation from polar to cartesian. r = sin 0 – 2 cos 0 -

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Q: 6 Rewrite the polar equation r = as a Cartesian equation (rectangular) 1 – sin(0)

A: We have the relation between polar coordinates and rectangular coordinates as x=rcosθy=rsinθ