a) Write the following equations in Cartesian coordinates and identify the figures they describe. i) r= cscocot0 (Cylindrical coordinates) ii) cotø = cose – 3 sin0. (Spherical coordinates)

Q: 9. Convert the rectangular coordinates (-1,2, –1) to spherical coordinates

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Q: Replace the polar equation with an equivalent Cartesian equation. r 2 = 26r cos θ - 6r sin θ - 9

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Q: 5 equally spaced holes on an 80mm pitch circle diameter. Calculate their co-ordinates relative to…

A: we know that, the total sum of angles in circle= 360 so now using this we will solve the question.

Q: Find the area of the circle given by r = sin θ + cos θ. Check your result by converting the polar…

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Q: Consider the spherical equation given by p = 4 cos 0 sin $. Determine its corresponding equation in…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: What is the reason that degrees is used rather than radians in a spherical coordinate system?

A: Solution: We have given that spherical coordinate system and have been asking that the reason behind…

Q: Lucy is riding a Ferris wheel with a radius of 40 feet. The center of the wheel is 55 feet off of…

A: Given: The radius of the Ferries wheel is 40 feet. The center of the wheel is 55 feet off the…

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: The expression p sin ø cos 0 in spherical coordinates is equivalent to what expression in Cartesian…

A: given expression ρsinφcosθ

Q: Convert the point (х, у, 2) — (— 4, — 2, 2) to - spherical coordinates. Give answers as positive…

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Q: State the formulas for converting rectangular to spherical coordinates.

A: Converting rectangular to spherical coordinates.

Q: Find the exact length of the polar curve. r = 6 sin ?,    0 ≤ ? ≤ ?/3

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Q: Write the equation in spherical coordinates. (a) 5z2 = 8x2 + 8y2 (b) x2 + 3z2 = 7

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Q: The equation o=- in spherical coordinates represents sphere. Select one: True O False

A: Here, the given equation is: φ=π5

Q: Convert the following point from rectangular to spherical coordinates:

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Q: Convert the following point from spherical to rectangular coordinates: 5, 4' 6 (х, у, 2) —

A: Use the following equations to convert spherical coordinates ρ,θ,φ to rectangular coordinates x,y,z.…

Q: In each part, find polar coordinates satisfying the stated conditions for the point whose…

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Q: The Cartesian equation equivalent of polar equation r = 4tane sece is y True False O

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Q: Convert the following from rectangular (Cartesian) coordinates to spherical Coordinates. (-V3, -3,…

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Q: Find an equation in rectangular coordinates for the spherical equation p = 6 cos(4)

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Q: find the equation of the cicles in standard form given the following conditions  a) center= (0,0) ;…

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Q: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.) 9(2…

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Q: Find the rectangular coordinates of the center of the sphere p = 2 sin w (cos 0 – 2 sin 0).

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Q: Convert the Cartesian coordinate (4,2) to polar coordinates, 0 ≤ θ < 2π.   r= ?? (exact value) θ…

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Q: Convert the Polar coordinate (2,5pi/4) to Cartesian/rectangular coordinates. X =? Y =? Enter as…

A: Polar coordinate 2,5π4

Q: Replace the polar equation with an equivalent Cartesian equation. r= 40 sin 0

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Q: 4. The boat is travelling at 18 knots on a heading of 234°. The current is 8 knots, flowing from a…

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Q: Translate the spherical equation below into both cylindrical and rectangular coordinates.…

A: Let x=r sinφ cosθ, y=r sinφ sinθ, z=r cosφ. Notice that xz=tanφ cosθ and yz=tanφ sinθ. Further,…

Q: Find the lengths of the curves given by the polar coordinate equations r = 2 sin θ + 2 cos θ, 0 ≤ θ…

A: Given: r=2sinθ+2cosθ; 0≤θ≤π2 for finding length of curve given by the given polar equation, first we…

Q: p = 4 cos 0 sin o

A: There exists a relationship between the cartesian and spherical coordinates. Using the relationship…

Q: 1 r = sin 0-4 cos 0

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Q: see attachment

A: We have to convert (-6, -4pi/3) to positive values. First add 2pi with angle to make it…

Q: Lucy is riding a Ferris wheel with a radius of 40 feet. The center of the wheel is 55 feet off of…

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Q: Translate the spherical equation into cylindrical coordinates Equation: tan2(φ) = 1

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Q: 5) (2,0°) -3 (4) 7) 4 ---22 -1 2 + 21 -1 D | x

A: We know that if r, θ is the polar coordinates then the rectangular coordinates is r cos θ, r sin θ.

Q: ind the rectangular coordinates for the point (1,..) which is given in spherical coordinates, and…

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Q: Convert the equation cot 0 csc 0 from polar to cartesian. r

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Q: the center of the circle given by the equation r = 6sinθ – 8cosθ in polar coordinates is M(a, b) and…

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

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Q: Convert the following point from Spherical Coordinates to Rectangular Coordinates.13 (ahải 2)

A: ρ, θ, ϕ=4, π4, π3 Therefore, ρ=4, θ=π4, ϕ=π3

Q: Consider the Cartesian coordinate point (3,2,1) Convert to spherical coordinates.

A: Consider the provided question, Given, Cartesian coordinate point (3, 2, 1). We need to convert into…

Q: Show that the polar equation r = a sin θ + b cos θ where ab ≠ 0 represents a circle, and find its…

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Q: What is the polar equation of a circle of radius a centered at the origin? Use this equation to…

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Q: Given the polar equation r2 sin20 = 8, find an equivalent Cartesian equation.

A: Given the polar equation r2 sin 2θ = 8

Q: (d) Convert from spherical coordinates to rectangular coordinate (12, –7/4,0)

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