Sketch the circles . Give polar coordinates for their centers and identify their radii. r = 4 cos u

Q: Find polar equations for the circle. Sketch eachcircle in the coordinate plane and label it with…

A: Here, given equation is x2+(y+7)2=49 By substituting x = r cos theta and y = r sin theta By…

Q: Find Cartesian equation for the circle. Sketch circle in the coordinate plane and label it with both…

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Q: Find the polar coordinates, 0 … theta .... 2pi and r >/ 0, of the following points given in…

A: (-3,4)

Q: In polar coordinates, the graphs of r = a cos θ and r = a sin θ are_______ .

A: r=acosθ⇒r=a·xr   ∵x=rcosθ⇒r2=ax⇒x2+y2=ax   ∵r=x2+y2 This represents equation of a circle. Similarly,…

Q: The following polar equation describes a circle in rectangular coordinates: r = 4 sin 0 Locate its…

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Q: Find the length of the following polar curve. The complete circle r= a sin 0, where a >0 The length…

A: Concept : given r ; the length of polar curve is ∫abr2+drdθ2dθ where a≤ θ ≤b given r= a sin(θ) as…

Q: Find the polar coordinates, -pi … theta .... 2pi and r </ 0, of the following points given in…

A: We have r=x2+y2=12+0=1 As we need r≤0, we take r=-1. We know that the angle between the ray through…

Q: Replace the polar equation with equivalent Cartesian equations. Then describe or identify the graph.…

A: We have, the given polar equation as rsinu=lnr+lncosu        ⋯⋯1 As we know that, the relationship…

Q: Find polar equations for the circle. Sketch eachcircle in the coordinate plane and label it with…

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Q: Find the polar coordinates, -pi … theta .... pi and r >/ 0, of the following points given in…

A: Here we have ;  Cartesian coordinates = (0,3)

Q: Given the rectangular coordinates (6, −6), convert to exact polar coordinates.

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Q: Evaluate the polar coordinate (3r sin 0)rdrde. Answer:

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Q: Find polar equation for the circle. Sketch circle in the coordinate plane and label it with both its…

A: Given,      x+22+y2=4

Q: Given the polar coordinates (4 , 2pi/3), convert to exact rectangular coordinates.

A: Given  polar coordinate (r,θ) = (4,2π/3) To find   Rectangular coordinate (x,y)  Method  x= r cos(θ)…

Q: Find the lengths of the curves given by the polar coordinate equations r = -1 + cos θ

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Q: Find the exact length of the polar curve. r = theta2,    0 ≤theta ≤ 7pi/4

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Q: Find the polar coordinates, 0 … theta .... 2pi and r >/ 0, of the following points given in…

A: The given Cartesian coordinates is (1, 1).

Q: Graph the polar curve given by: r= cos (30)

A: Remember the theorem: A curve in polar coordinates is symmetric about x-axis if replacing θ by -θ in…

Q: Sketch the following polar rectangle. R= sos Choose the correct graph below. O A. OB. OC. OD.

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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: Find the Cartesian coordinates of the given polar coordinates. Then plot the point. (-sqrt2, 5pi/4)…

A: Given: ( -√2 , 5π/4 )  ( 1 , 5π/4 ) (4 , -7π/6 )

Q: Find the area and circumference of the circle represented by the polar equation r = 6 cos 0 using…

A: The given problem is to find the area of circle and circumference of the circle for the given circle…

Q: State the name of the shape that is created by each polar equation: a) r= a-asin e b) r cos e = a C)…

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Q: Determine in polar coordinates the center and radius of the circle r2 + 4r cos(θ) − 4√3 r sin(θ) −…

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Q: Convert the following polar curves into Cartesian, tehta = pi/3

A: Converting polar curves into Cartesian,

Q: Show that the polar equation r = asin(θ)+ bcos(θ), where ab≠0, represents a circle, and find its…

A: We have to proof

Q: What kind of the polar graph has the equation r = 2 + 2 cos 0? limacon cardioid lemniscate…

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Q: Given a point P represented by the ordered pair (r, θ) in polar coordinates, the distance from P to…

A: Given: A point P represented by the ordered pair (r, θ) in polar coordinates, the distance from P to…

Q: What kind of polar graph has the equation r = 3 ? * cardioid lemniscate circle rose petal

A: Solution: equation r=3

Q: Convert the given polar equation to a Cartesian equation. (Use the following as necessary: x and y.)…

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Q: A Imaginary Real

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Q: Plot the following points, given in polar coordinates. Then find allthe polar coordinates of each…

A: Given: The following graph shows the plot of a point in a polar coordinate,

Q: Use a calculating utility, to approximate the polar coordinates of the points whose rectangular…

A: A)(x,y)=(3,4)r=x2+y2r=32+42r=25r=5θ=tan-1yxθ=tan-1(43)θ=53.13°B)(x,y)=(6,-8)r=x2+y2r=62+(-8)2r=100r=…

Q: Complete the table of coordinates below. Where necessary,round to two decimal places. Then plot the…

A: we use the trigonometric values for cosθ to find out the coordinate r for each θ .

Q: plot the given polar points (r,theta) and find their rectangular representation  (5, - pi/2)

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Q: The polar coordinates of a point are given.  Plot the point.   (4, 5pi/4)

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Q: Transform the given polar equation to retngulr coordinates and identitythe cuve represented 5+4x y =…

A: The answer is found in step-2

Q: Find the Cartesian coordinates of the following points (given in polar coordinates). a. (0, pai/2)…

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

Q: Match each point in polar coordinates with either A, B, C, or D on the graph. Co 5T 10,- 11x 10. 11x…

A: To find the polar coordinates of the point specified.   C is the reflection point of A, so…

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: 5. Convert the polar equationr= cot 0 csc 60 to rectangular form.

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

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: Find the exact length of the polar curve. r = 3 cos(theta),    0 ≤ theta ≤ pi

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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: Convert the polar equad-lon to rectungular form r "sec o =p? tan?o sece -ręcs EG

A: To convert the polar form into rectangular form