Convert the rectangular coordinates to polar coordinates with r>0 and 0 s 0< 27. ])-«

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

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Q: Transform the polar equation r = 3 sin(0) to an equation in x and y. %3D

A: Converting the polar equation to rectangular equation

Q: Write a polar equation of the form r sin(0 – 0,) = ro for the line 2/3 x+2y = 1. %3D

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Q: Convert the equation rsin 0 = ln r + ln cos 0 from polar to cartesian.

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Q: What are the rectangular coordinates of the point with polar coordinates (r, 0) =(-6, ?

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

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

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Q: snip

A: Polar system is a two-dimensional system . "r" is the distance of the point from the origin .  θ is…

Q: Use polar coordinates to calculate e-(z²+y²) dydx. roo Express -(2²+y²) dydx in terms of dr, and…

A: We will find out all the required values.

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates.

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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: Consider the point ( 4v2, ) 57 in polar coordinates. What are the corresponding rectangular 4…

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Q: 5. Find two sets of polar coordinates for the Cartesian point (-7, 7/3) such that 0<0<2T.

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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: True or False In the polar coordinates (r, θ), r can be negative.

A: Consider the following statement: " In Polar coordinates r,θ , r can be negative"  Determine the…

Q: The rectangular coordinates for the polar points (4, 2 is (0, —4) о (4, 0) o (-4, 0) o (0, 4) o

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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: Find the distance between the two points (2, 0.5), (7, 1.2) in polar coordinates.

A: Here, we have given two points in the cartesian coordinate system (x, y). So,…

Q: Convert the point (3, V5) from rectangular to polar coordinates with 0 < 0 s a/2. (Round your…

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Q: Give two polar representations for the point (x, y) = (0, 1), one with negative r and one with…

A: Check the polar representation.

Q: Convert the polar equation to rectangular form and sketch its graph. r = 3 sin(0) y 3.0 y 2.5 2 2.0…

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Q: b. Express the point in at least two different ways. (Since polar coordinates are not unique.) (2)-(…

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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: Sketch and find additional polar three points for (2,4pi/3). When r&gt;0 and r&lt;0. And theta is…

A: Given polar coordinate:

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

A: The length of the polar curve r(θ) for a ≤ θ ≤ b is given by,

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

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Q: What are the polar coordinates (r, 0) of the point with Cartesian coordinates (x, y) = (v2, – V2) ?…

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Q: Express the Cartesian coordinates (-3/3,-3) in polar coordinates in at least two different ways.

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Q: find the area of the polar curve.   r=3-sin@

A: To calculate the area of the given polar curve , using integration

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: Transform (0, y) from rectangular into polar form (here y is any negative number).

A: We have convert rectangular coordinates (0 , y) into polar coordinates: Where y is negative number-

Q: 6. Convert 5,5/3] to polar coordinates with r positive and between 0 and 27

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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: Does the origin lie on the polar curve r = 1 – 3cose ? Explain.

A: We will first plot the polar curve in the 2D (r,θ) plane with polar coordinates. We shall plot it…

Q: What are the polar coordinates (r,θ) of the points of intersection of C1 curve with polar equation…

A: It is given that, It s known that at the point of intersection equation of both curves satisfies…

Q: 1. What are the rectangular coordinates of the point with polar coordinates (r, 0) = (10, 45°)?

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Q: Find two sets of polar coordinates for the Cartesian point (-1, -v3).

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

A: r = 3            a vector of length '3'. θ = -3π4  '-ve' : Rotate clockwise by 3π4…

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

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Q: onvert the Cartesian coordinate (4,3) to polar coordinates, 0 < 0< 2n

A: We have to convert the cartesian coordinates (4, 3) into polar coordinates, 0≤θ≤2π.

Q: Consider the spherical equation given by p sponding equation in Cartesian coordinates. 4 cos sin o.…

A: The given spherical equation is ρ=4cosθsinϕ To convert the spherical equation to cartesian…

Q: 1. Convert the Cartesian coordinate (12,5) to polarcoordinate.

A: Given the cartesian co-ordinate(x,y)=(12,5)

Q: Write polar form of z=-2-i V5 (cos2.68 – i sin2.68) 5(cos2.68 – i sin2.68) V5 (cos2.68 + i sin2.68)…

A: The objective is to write the polar form of complex number z=-2-i

Q: Describe the test for symmetry with respect to the polar axis.

A: The graph of a polar equation is symmetric with respect to the polar axis if replacing r, θ with r,…

Q: What are the polar coordinates (r, 0) of the point with Cartesian coordinates (x, y) = (V2, -V2) ? ㅇ…

A: Given cartesian coordinates:x,y=2,-2To find: polar coordinates r,θ

Q: roblem 1: onvert from rectangular to polar form: a) 2 + 2v3i b) 3- 4i =) V3 - i

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

Q: Find the rectangular coordinates of the point(s) of intersection of the polar curves r= 2 sin(2 0)…

A: This question is based on conversion of polar coordinates to rectangular Cartesian coordinates.

Q: Transform the polar equation 0 to an equation in a and y. %3D 4

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Q: converts from cartesian coordinates (x, y) to polar coordinates (r, theta).

A: To convert Cartesian coordinate of any point (x, y) to polar coordinate (r, θ) We will use x = r…