2. r= 1+2 cos 0 2т 3 2 3 Check for symmetry polar axis line 0 pole EIN

Q: Find the length of the polar spiral r = 0² from 0 < 0 < V5.

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Q: What is the area of the area Outside the polar curve r= 1+ cosoo and inside the polar curve r=3 cos…

A: Given : Polar curves Cardioid r = 1 + cos θ, Circle r = 3 cos θ     To find : Area of the outside…

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A: Symmetry around the polar axis (x-axis): Replace θ  with - θ  We have the given equation in polar…

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: 24. Which of the following polar curves is a cardioid? A. r= cos () B. r= 2+3sin® C. r = 3– 20ose…

A: 24)      A. r=cos2θ2                                                         B)r=2+3sinθ…

Q: Find z1 /z2 in polar form. z1 = 16( cos(110°)+i sin(110°)); z2 = 2( cos(40°)+i sin(40°))

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Q: All the polar coordinates of the point (4,) are: (o) (+종+ 2am) amd (-+종+ 2am) (6)(4 + 2) and (-4 +…

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Q: 2. Write z = -ói in polar form. O z = 6cis= 2 O z = 6cis- Oz =-6cis- 2 Oz = 6/2 cis 37 2 3. Write z=…

A: Let, z= 6 (cos(π/2) +isin(π/2))  or, z=6cis(π/2)

Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: compute the length of the polar curve. The length of r = θ2 for 0 ≤ θ ≤ π

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Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

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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: Find the slope of the tangent line to the polar curve r= cos( =: os(20) when 0 3

A: Given: Equation of the polar curve   r = cos(2θ)       To determine: The slope of the tangent line…

Q: 20) Find two sets f polar coordinetes, (r, o),0LOL2 IT Por the point (6,6) in recten- gular…

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Q: (Picture of question is attached)

A: Calculate the values using the given polar equation and complete the table.

Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: Draw the polar curve r = cos(30) with its orientation. Set up all integral to evaluate the length of…

A: First, find the node to the polar curve by equating r = 0, so cos(3θ)=rcos(3θ)=0(3θ)=-π2,π2θ=-π6,π6…

Q: Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the…

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

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Q: 2. Determine the area of the region that is simultaneously interior to the curve r = 2 + cos (38), e…

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Q: 13) Find as all polar points (r, 0) of horizontal and vertical tangency to the curve: x = cos(20) y…

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Q: Find the area of the inner loop of the limacon with polar equation r = 5 cos 0 – 2 -1 = COS (금)

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Q: test for symmetry and graph polar equation

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Q: Find the area of the inner loop of the limacon with polar equation r = 5 cos 0 – 2 y (음) = COS

A: We have to find the area of the inner loop of the limacon with the polar equation r=5cosθ-2. with…

Q: Compute the length of the polar curve. r = 1 + θ for 0 ≤ θ ≤ π/2

A: It is given that,  r=1+θ  for    0≤θ≤π2

Q: A tangent at the pole to the polar curve r = is 2-4 sin 0 A 0 = = af pole usin6-2 Sing D 0=

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Q: Divide. 6√5cis (11) + 3√6cis (5) Drag a value into each box to correctly express the quotient in…

A: Given the query is to find the value of the expression.

Q: What is the length of the polar curve r = 7 sin 0 from 0 = 0 to 0 = 2n? Enter a numerical value…

A: Length of the polar curve = ∫θ=αθ=βr2+drdθ2 dθ

Q: Find the number of points of intersection of the polar curves r=2cos0 and r=1+2sin0. O 1 3 O 2

A: Number of point of intersection of polar curves r=2cosx and r=1+2sinx

Q: Which of the following is the distance from point. A( V5, 0) to point B(2V10, Y) in polar…

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Q: iyı , Z2 = x2 +iy2 than Z,Z, in polar forr + 62) – i sin(0, + 02) Z,Z2 = ir2(cos(0, – 02) + i sin O…

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Q: 1z2 in polar form. z1 = 5(cos(170)+i sin(170)) : z2 = (1/2) (cos(10)+i sin(10)

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Q: 1. How many petals does the polar curve r=5cos(6theta)?  2. At what points the curves…

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Q: 44. A tangent at the pole to the polar curve r = 2- 4 sin 0 is af pole 0 = = D 0 = Sing 8sin

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Q: Consider the polar curve r=2sin(30) for 0s0sn.

A: Given polar curve is r=2sin3θ for 0≤θ≤πfind the area of the region inside the curve

Q: Calculate the length of the polar curve r=1- sin Oon the given interval (0, 2m].-

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Q: If Z, = (-V3 + 3i), Z2 = (2+ 2i ) than 4 in polar form is : %3D Z2 Z1 5n 5n (cos +i sin 12 5n (cos…

A: z1=-3+3i,z2=2+2i,z1z2=-3+3i2+2iApply complex arithmetic rule:  a+bic+di = c-dia+bic-dic+di =…

Q: Find the points of horizontal tangency to the polar curve. r 2 csc 0+3 050<2x (smaller r-value) (r.…

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Q: Find z1z2 in polar form. = 4 (cos(140°)+i sin(140°)); z2 = (cos cos(40°)+i sin(40°) Z1

A: We use the fact that  Cost+ i Sint = eit

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: Calculate the length of the polar curve r =1- sin Oon the given interval [0,2m).

A: The arc length can be calculated using the formula L=∫abds. Here, a and b are the upper and lower…

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

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Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: 2. (a) Convert (5/3, , –5) to polar corodinates with r > 0 and then with r < 0.

A: If cartesian coordinates are (x,y) then polar coordinates are (r,θ), where  r2=x2+y2tan θ=yx Here…

Q: Plot the polar curve r=2(1–cos0) in interval

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Q: Find the area of the region. Interior of r = 4 + 3 sin 0 (below the polar axis)

A: Given that         r = 4 + 3 sin (theta) Here we have to find the area of the region below the polar…

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: (Picture of question is attached)

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Q: Calculate the length of the polar curve r = =1-sin Oon the given interval [0, 2m].

A: Given the polar curve r=1-sinθ over the interval 0,2π