5. Consider the point with rectangular coordinates (1, – V3 ). sState the coordinates of the point in polar form, with 0° < 0< 360° and r>0. Let's try that again (2, 240°)

Q: r = 2 cos 0,

A: To find the exact length of the polar curve.

Q: A Cartesian equation for the polar equation r 8 can be written as: %3D x2 + y?

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Q: Sketch the polar curve r= Jcos 20 and r = 2cos0. %3D

A: To sketch the polar curve r = cos 2θ   and r = 2cos θ

Q: Find the exact length of the polar curve described by: 9e -0 on the interval

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

A: Polar coordinates.

Q: Consider the curve given in polar coordinates by r = 2 – sin 0. Compute the slope at 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: Sketch the curve with polar equation r = 2sin3θ.

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Q: Give two possible pairs of polar coordinates (r, 0) for the rectangular (Cartesian) point (-6, –6V3)

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Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

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Q: Sketch the following polar rectangle. 2x = {(r,0): 4sr5,

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Q: Find the exact length of the polar curve. r = = 02, 0 < 0 < 3t/4

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Q: Determine the shape of each polar curve. 9r = 7 parabola 7 circle 9 r = 4 + 6 sin(0) ellipse…

A: Given :            r=7r=74+6sinθr=74+4sinθr=76+4sinθ

Q: Under what conditions can you find the length of a curver = ƒ(θ), a ≤ θ ≤ b, in the polar coordinate…

A: step 1 :           Conditions to find the length of the curver = f(θ) , ∝ ≤ θ ≤ B* The curve r =f(θ)…

Q: Find a polar equation for the curve represented by x2 + y2 = 8cx, where c is a constant.

A: The given equation is x2 + y2 = 8cx   Known fact x=rcosθy=rsinθ

Q: Find a polar equation for the curve represented by the given Cartesian equation. x2+y2=100

A: Here given cartesian equation  x2+y2=102 it is an equation of the circle with radius 10.

Q: Plot the points with polar coordinates 4, and 3, using the pencil. 4 2n 3 4 0. 4. 9. 11n 9. 5T 4 4…

A: Topic:- Geometry

Q: Find the exact length of the polar curve. r = 02, 0 < 0 < 3t/4

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

A: Given,             r=6sin4θ , θ=0

Q: Sketch the curve r = 8+8cos € in polar coordinates.

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Q: Q1 Find the polar coordinates of the Cartesian point (2,2)

A: We have to find the polar coordinates of the Cartesian point ( 2, 2 ).

Q: Sketch the polar curve defined by the equation r =1+2cos(3t).

A: We will sketch the polar curve by finding the value of ' r ' for different ' t ', t varies from 0 to…

Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

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Q: Find the exact length of the polar curve described by: r = 5e-0 %3D 7 on the interval

A: The given function is r=5e-θ, where  7π2≤θ≤6π. The length of the polar curve is obtained by the…

Q: Find a polar equation for the curve represented by the given Cartesian equation. x² + y2 = 16

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Q: Draw the following Polar Curves:- 1. r= a cose

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

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: Convert the rectangular equation to polar form and sketch its graph. y = 6 6 T/2 T/2 12 15 10 8 10 4…

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Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: Find the distance between P1(1, –91°) and P2(3, 335°) on the polar plane.

A: We know that, Distance between two Cartesian coordinates is,  Distance , D=x2-x22+(y2-y1)2 We know…

Q: Mark the alternative that corresponds to the radius R and the center C (in polar coordinates (r,θ))…

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Q: Derive the formula for the distance between points P1(p1,q1,z1) and P2(p2,q2,z2) given in spherical…

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Q: and (5, a) using the pencil. 3 -6, - Plot the points with polar coordinates ? 01 l1x 4. tien 2.

A: The point A(5,π) is plotted at the radial distance of 5 units and positive angle of π as shown…

Q: find the slope of the tangent line to the polar curve at the point:

A: From the given expression we find

Q: The alternative polar coordinates that satisfies r 0 for

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Q: (4, − 19π/12)   plot the point with the given polar coordinates

A: The given point is 4,−19π12. The general form of the polar coordinate is r,θ where, r is the…

Q: The point specified by the polar coordinates (7.00, 35.0°) is following when converted to Cartesian…

A: Calculating the cos and sin theta  cos(35o) = 0.81915sin(35o) =0.5736

Q: Find the length of the polar curve r = −4 sin θ, 0 ≤θ ≤π. Assume that the curve traces out exactly…

A: Find the length of the polar curve r = −4 sin θ, 0 ≤θ ≤π. Assume that the curve traces out exactly…

Q: Find polar Ir>0 and Os0<2T. Coordinates of the points such that

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Q: Determine the length of the polar curve r = 2°, 0<0<.

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Q: Calculate the slope of the polar curve  r=4cos3θ  at the point where θ=5π/6

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Q: 2. Convert from a rectangular equation to a polar equation. x = 2y2

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Q: Q. A) Replace the following polar equation by equivalent Cartesian equation: rcos (0 - ) = 3

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Q: Find the polar equation of the line y = 3x + 9 in terms of r and ?.

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Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: 3. Change (r+1)²+y² = 1 to an equiv- alent polar equation

A: GIVEN (x+1)2+y2=1

Q: Find the length of the polar curve r = 5°; 0 <e< 2n

A: Given ,r=5θdifferentiate w.r.t.θdrdθ=5θ.ln(5)Weknow that length of the curve…

Q: Find the exact length of the polar curve described by: r = 7e-0 3 on the interval 10

A: r=7e-θ,    310π≤θ≤6π Differentiating with respect to θ, we get drdθ=7-e-θ=-7e-θ