• Make your own artwork on symmetry • 1 artwork - symmetric with respect to 0 = ", (y – axis) | 2 • 1 artwork - symmetric with respect to the polar axis • 1 artwork - symmetric with respect to the pole

Q: 4. r2 = 9 sin 20 π TT TT 4 3. 2 r Check for symmetry polar axis line 0 = pole

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Q: Find all the roots of z² = 1 + i in the polar form rei®. Sketch the graph of the cardioid r = 1+ cos…

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Q: Test for symmetry with respect to a. the polar axis, b. the line 0 =, and c. the pole. 2' r= 5+3 cos…

A: We have to check the symmetry for the given curve…

Q: Find the Cartesian equation of the polar equation. rsin 0 = 3 4 The Cartesian equation for r sin 0 4…

A: Given polar equation is r sinθ-π4=3find the cartesian equation

Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan…

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Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

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Q: 9. Approximate the surface area of the surface generated by revolving the polar curve given below…

A: I have appended the formula used in the solution part

Q: Use a graphing utility to find one set of polar coordinates (r > 0, 0 se < 2n) of the point given in…

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Q: Q1 Find the points of intersection of the polar curves rcos and 2-cos-r=0 Q2 Find the points of…

A: Introduction: The polar curve has the form r=fθ. When two polar curves intersect each other, the…

Q: Use the integration capabilities of a graphing utility to approximate to two decimal places the area…

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Q: Interior of r = 9 – sin 0 (above the polar axis) -

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Q: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

A: To solve the following problem

Q: 3. Find two different sets of polar coordinates (r. 8) for the point with Cartesian coordinates (x,…

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Q: Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that…

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Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

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Q: 4. Consider the point in the plane given by polar coordinates (r,0) = 3 - (2. 증). (a) Express this…

A: Definition used -           A point r,θ in polar coordinate can be written in an…

Q: Consider the polar curves r = 4 cos 0 and r = sec 0. a. Find the polar coordinates of all…

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Q: 16 (1+ v3) ( v3-1)" Evalute 7 by de Moivers theorem, using polar form calculations.

A: Note  your Question is wrong because in numerator imaginary part missing  so i  try to solve this…

Q: 7. Test the polar equation r = for symmetry with respect to the polar axis, the pole, 1+3 cos 0 and…

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Q: Find two other pairs of polar coordinates of the given polar coordinate, one with r>0 and one with r…

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Q: Test the polar equation for symmetry with respect to the polar axis, the pole, and the line 8 = I.…

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Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

A: Given r=4cos2θ and 0≤θ≤π4 To find the area of the surface formed by revolving the polar equation…

Q: Test r2 = 16 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ= π/2.  c) the…

A: (a) To test for symmetry in polar coordinates with respect to the line θ=π/2, replace (r, θ) with…

Q: r2 = 16 cos 2θ.Test for symmetry with respect to:a. the polar axis. b. the line θ =π/2. c. the pole.

A: We have the  polar equation given as r2=16cos2θ (a) Now testing for Symmetry about polar-axis,…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,n2, n3),B(m,m2,m,),C(r..). 2.…

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Q: Test for symmetry with respect to the line 0 = t/2, the polar axis, and the pole. (Select all that…

A: It can be find by putting the required condition of curve and the angle.

Q: The slope of the tangent to the polar curve r 2 sin(0) at 0 = is O- V3 None of these 1 V3 V3 1 V3…

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Q: Test for symmetry with respect to the line 0 = t/2, the polar axis, and the pole. (Select all that…

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Q: For the polar equations r1=1-cosx and r2=1, (1)sketch the graphs of r1 and r2 in the same coordinate…

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Q: Test r2 = 9 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ = π/2. c) the pole.

A: Test r2 = 9 cos 2θ for symmetry with respect to a) the polar axis. b) the line θ = π/2. c) the pole.

Q: Consider the polar curves r = 3 and r = 3 + cos 3θ. Both curves are symmetric about the polar axis.…

A: We have to set up the integral for the given region.

Q: Test for symmetry and graph polar equation

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Q: Use a graphing utility to find one set of polar coordinates (r > 0,0 s 0 < 2n) of the point given in…

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Q: 6 Find three additional polar representations of the point, using -2n < 0 < 2n. (Enter your answers…

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Q: Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that…

A: Given polar curve: r=6+4cosθ We have to test the symmetric of the given polar curve.

Q: 10. LARPCALC10 10.7.011. MY NOTES ASK YOUR TEACHER Plot the point given in polar coordinates. (-7,)…

A: Consider the given point as -7, 2π3

Q: 2. Consider the two polar curves r = 1 and r=2+2 cos(0). 2.1. Find polar coordinates for all points…

A: 2. The given polar curves are r=1 and r=2+2cosθ To find: 1. intersection point of two curves.…

Q: Paove that the distane, b, points with between two polar coordinates (s, Bq) aud (s2,E2) is…

A: TO PROVE : THE DISTANCE BETWEEN TWO POINTS WITH POLAR COORDINATES s1 , θ1 AND s2 , θ2  IS…

Q: II. Consider the polar curves C : r =2 with respect to the polar axis. Let P and Q be the points of…

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Q: 11 Final the directrix of the polar curve r = 9-2 cos 0 11 99 x = 2 99 2 0 x = - 11 x = -

A: To find- directrix

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

A: Calculation:

Q: Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that…

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Q: 3. (a) Sketch the graph of the cardioid r=1+sin@ and the circle r= 3sin0. (b) Shade the region that…

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

Q: Both the polar curves r 3-2cose and r=-3+2 cos0 are symmetric to what axis O Line OX or the polar…

A: To find the symmetry of both the curves, r=3-2cos θ and r=-3+2cos θ, plot the graphs of both the…

Q: Use a graphing utility to find one set of polar coordinates (r > 0, 0 s 0 < 27) of the point given…

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Q: (32) is not a representation of the point (4,) in polar coordinates. -(33) is the polar equation…

A: *Two different co ordinate will represent same point if they  coincides  * general equation of…

Q: Use a graphing utility to find one set of polar coordinates (r > 0, o se < 2n) of the point given in…

A: we know  r= √(x2+y2)  θ depends on quadrant of given rectangular coordinate

Q: (Picture of question is attached)

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Q: Test r2 = 16 sin 2θ for symmetry with respect to a) the polar axis. b) the line θ= π/2  c) the pole.

A: Consider r2=16 sin 2θ . . . . . .(1) (a) Replace (r,θ) with (r,-θ) we get r2=16 sin 2-θr2=16 sin…