Q1) A) Replace the polar equation r? sin 20 = 2 by equivalent Cartesian equation. B; C) Find the shared area between the circle r = 2 and the cardioid r = 2(1- cos 0) in the first quarter. %3D s)

Q: Write in Polar form: r(cosθ+isinθ)r(cosθ+isinθ). (0≤θ<2π0≤θ<2π and round to 3 decimal places)…

A: Given:     z = 8 + 10i    0≤θ&lt;2π

Q: polar curves intersect at right angles.

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Q: The propellers for a toy boat are manufactured by stamping out a rose with n petals and then bending…

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Q: Find the area of the region. Interior of r = 10 + 7 sin 0 (below the polar axis)

A: Explained below

Q: a) Reproduce the algebra required to convert this Cartesian equation to the polar form r = sin(20).…

A: Given the algebraic equation, (x2+y2)3=4x2y2 ⋯⋯(1) (a) Take x2+y2=r2, x=rcosθ, and y=rsinθ Then…

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

A: .

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: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) 9 + 7i r = • 0…

A: The given complex number is: z=9+7i

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

A: Polar coordinates.

Q: Find the circumference of a circle described by the parametric equations = 7 cos 0 and y = 7sin 0…

A: The formula L=∫dxdθ2+dydθ2dθ is formula for length of arc in polar coordinates. As we go along the…

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

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Q: Convert the following polar curves into Cartesian. r= 2/(4-costehta)

A: Converting polar curves into Cartesian: r2 = x2 + y2 x = rcos θ y = rsin θ

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: 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: Write in Polar form: r(cosθ+isinθ). (0≤θ<2π and round to 3 decimal places) 8+10i r= , θ=

A: The polar form of a complex number z=a+bi is z=r(cosθ+isinθ). where, r=|z|=a2+b2 , a=rcosθ  and…

Q: Find a Cartesian equation from the polar curve 4r sin 0 = 18(rcos 0) +14 1S is

A: Given polar equation is 4rsinθ=18rcosθ2+14  .....1

Q: How many petals are there in the graph of the polar equation r = 2 cos3@ ?

A: Draw the polar curve

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: The magnitude of area inside of polar curve (r =) and outside 2 of polar curve (r = sin0) is equal…

A: We have to find the magnitude of the area inside of the polar curve r=3π and outside of the polar…

Q: Write in Polar form: *(cos e + z sin 8). i sin 0). (0 < 0 < 2n and round to 3 decimal places) - 17 +…

A: We have to find value of r and θ Consider ,z=-17+12iHere x=-17 and y=12 Here we will use the…

Q: Find the Slope of the polar urve at the indicated pont r= 6 sin 4e

A: Given,             r=6sin4θ , θ=0

Q: Find the slope of the tangent line to a given polar curb at the point specified by the value of…

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Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) — 12 — Зі r =…

A: Given: -12-3i. The objective is to write the polar form.

Q: If a point is represented as (x,y) in the Cartesian plane and (r,0) in the polar plane, then 0 = tan…

A: A point in cartesian plane is (x,y) and (r,θ) in the polar coordinate, then θ=tan-1yx.

Q: Replace the polar equation r2 sin 20 = 2 with equivalent Carte sian equation %3D

A: Given, The polar equation  r2sin2θ = 2    We have to write the equivalent cartesian equation.

Q: Sketch the polar curve r = sin? 0.

A: We have given a curve; We have to plot the polar curve on;

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

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

Q: If an equation fails the test for symmetry with respect to the polar axis, what can you conclude?

A: The equation has failed the symmetry test, but that does not mean that it is not symmetric with…

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: Sketch me polar urve =cos(60) %3D and wmpute the tangent linm ar thm Value = 24 TT

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Q: Find the area of the region inside one leaf of the polar graph: r = sin7x

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Q: What is the polar equation of a circle of radius Va? + b centered at (a, b)?

A: General equation of a circle is given by - x-h2+y-k2 = r2              ..............(1)where,h, k =…

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

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Q: Find the exact length of the polar curve. 3 sin(0), 0 < 0< 1/2

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Q: Find the area of the region inside one leaf of the polar graph: r = sin4x

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Q: Convert the rectangular coordinates (4, 0) into polar form. Express the angle using radians in terms…

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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: 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: A) Replace the polar equation r2 sin20 = 2 with equivalent the Cartesian equation %3D

A: Given: The polar equation r2sin2θ=2, To find: Equivalent cartesian equation.

Q: Find the area of the region Interior of r = 9 − sin (above the polar axis)

A: we have to find the area above the polar axis which means θ varies from 0&lt;θ&lt;π

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

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Q: 7. What is the equation of the curve in rectangular coordinates whose equation in polar coordinates…

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

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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: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) 19 – 4i r = .0 =

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Q: Change the following rectangular equations to polar form. Show work on separate paper. 14. x² +y°…

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Q: Show that the polar equation for the curve with Cartesian equation x² – y² = 1 is r? = sec 20.4

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