If a point is represented as (x,y) in the Cartesian plane and (r,0) in the polar plane, then 0 = tan True O False

Q: The point P has coordinates x = 1 m and y= -1 m relative to the origin O and the vector v is as…

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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: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

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Q: Find the polar coordinates of the point with r> 0 and o ses 2n. (r, 8) = 2 0.5 1.5 2,5 3,5

A: Consider

Q: Write the polar equation in rectangular form. r = 6 sin 0 Oy =-6x Oy =x- 3 O x² + (v – 3)² = 9 O (r…

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Q: Find the rectangular coordinates of the point(s) of intersection of the polar curves r = 6 sin(0)…

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Q: What is the rectangular equivalence to the parametric equations? x (0) = 3 cos 0 + 2, y (0) = 2 sin…

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Q: Find the rectangular coordinates of the point P with polar coordinates (4, А. Р%3D (-4,4) В. P = (--…

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Q: Two points in the xy plane have Cartesian coordinates (2.00, -4.00) m and (-3.00, 3.00) m. Determine…

A: Distance between two points is given as:…

Q: express in polar coords with: Cりり me point whose Ty-Coords are a.r>o and OsoL2

A: Introduction: The polar coordinates r,θ of rectangular coordinates (x,y) in two-dimensional…

Q: osen y

A: Is it sen y =x

Q: Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.

A: Given:        r=2sin3u3,  0≤u≤3π

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: Find the length of the curve r = 2 sin^3 (u/3), 0<=u<=3pai, in the polar coordinate plane.

A: To determine the length of the polar curve.

Q: 2. Use calculus to show that these polar curves intersect at right angles. = sin 0, r = cos 0

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

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Q: 13 Convert x 2 + y 2 - 2x = 0 to a polar equation. r = 2cosθ r² = 2cosθ r = 2sinθ

A: We have to find the polar equation

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: If 0 < 0 < 7, which of the following points DOES NOT coincide with the polar point (-r, 0)? Select…

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Q: Find the areas of the regions in the polar coordinate plane described Enclosed by the limaçon r = 2…

A: The limacon is symmetric around the x-axis thus doubling the area of the part over the x axis gives…

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

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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: Find the points of horizontal tangency to the polar curve r = 2 csc    + 3 .

A: Consider the given curve , r=2cscθ+3 Find the points of horizontal tangency . The relations between…

Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.

A: The relation between polar coordinates r,u and rectangular coordinates x,y is x=rcosu…

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

A: We have to find

Q: 2. Express in true polar form, z 5(cos 55°-j sin 55°)

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Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

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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: 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: 30. Determine two sets of parametric equations for the line passing through the points P( 1,7, 1)…

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Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec θ

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Q: Write a polar equation of the form r cos(0 – 0,) = ro for the line x - y = v2. %3D

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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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

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Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

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Q: Convert the polar equation r- 3 cosa 5 sin A in Cartesian equation form. )x² + y² - 3x = 5y 1- 3x =…

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Q: Find the polar coordinates, -π ≤ θ &lt; π and r≤ 0, of thefollowing points given in Cartesian…

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Q: Convert the point Cr,e)f from polar to nectangular COordinates (xx) 5T 3. ब्लज( कथावक 2)(a,)

A: To convert the given point from its polar form to rectangular form

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: 2. Use polar coordinates to evaluate 2 1. √4+7++5² dy dz. Jo

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Q: Find the corresponding Cartesian equation of the parametric equation       x=3cosθx=3cosθ.…

A: Given:           x=3 cos θ,   y=4 sin θ            0≤θ≤2π From: x= 3 cos θ            cos θ=x3 From:…

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: The rotation about the origin at an angle e=180° is defined by (ху)-(ху) (ху)-(ух) O (x.y)->(x,-y)…

A: The rotation about the origin at an angle 180° is defined by :-

Q: If the cartesian coordinates of a point are given by (3, y) and its polar coordinates are (r, 60°),…

A: This question can be solved using the concept of polar coordinates.

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.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.