Find an equation in x and y that has the same graph as the polar equation r- sin 0 = 0 and graph on the xy plane. 16.

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Given  equation r=2+3sinθwe have…

Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and - the…

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

Q: Q2 Q1 Find the points of intersection of the polar curves r-cos () = 0 and 2-cos A-r=0

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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: 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: 2. Find the length of the curve represented by the following polar equation. 15050을=4 1 r ==,0s0sI…

A: In the question we have to find the arc length.

Q: b) Find the slope of the tangent line to the given polar curve at the givén value of e: r=2 cose, e…

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Q: - A tangent at the pole to the polar curve = V2 – 2 cos0 is 0 = r = A 3

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Q: Consider the polar curves C₁ : r = 2 cos 0 and C2 : r = 2 cos 30, and let R be the shaded region as…

A: Given: C1:r=2cosθC2:r=2cos3θ To find: Area of the region

Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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Q: 3 4. Sketch the region described in polar coordinates by r < Cos e

A: We need to sketch the region.

Q: 1. Change to polar form, then evaluate: -x-1 х — у dydx V1-x² /x² + y² -1

A: Solution is given below..

Q: Consider the curve given in polar coordinates by r = 0 + cos 0 . Compute the slope at 0 = 0. %3D O…

A: Slope of polar curve r=f(theta) is given by dr/d(theta) Differentiating r with respect to theta we…

Q: (). 3 Calculate the length of the polar curve r = 8 sin' 3 in the interval 0 < 0<.

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Q: Assume 0 <0< T. The number of points where the two polar curves r = cos (0) and r = sin(0) intersect…

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Q: 3. Consider the curves given by the polar equations r = 2 and r = 4 cos 0.

A: r = 2 r = 4 cosϴ

Q: Find an equation in x and y that has the same graph as the polar equation r-sin 0 =0 and graph on…

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Q: 37. The Cartesian equation of the polar curve 2 = 2a' sin 20 is A. 1? + y? = 4a²xy B. (z* + 3° )° =…

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Q: 3) Sketch the polar curve r = 1 + 2 cos 0. In your graph, label the points corresponding to the…

A: See the attachment

Q: Plot the following curves in polar coordinates. 4. r r = sin() 5. r= 1 + cos 50 6. r² - sin 0

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Q: 2. Identify the coordinates of the point in polar form based upon the given conditions. Use pi for…

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Q: Q2 Find the points of intersection of the polar curves r=1+cos 9 and r= -cos

A: Point of intersection of the Polar curve

Q: 4. Find the exact length of the polar 2 cos os 0, 0 < 0 < T. curve r

A: Given: r=2cosθ on 0,π L=Length of Polar curve= ∫ab(r(θ))2+(r'(θ))2dθ now, r'(θ)=ddθ(2cosθ)=-2sinθ…

Q: Find the exact length of the polar curve described by: 0 r = 4e 5 on the interval 6 ≤0 ≤ 6.

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Q: Find dy/dr and the slopes of the tang ent lines shown on the graph of the polar equation r = 2+3 sin…

A: According to question, r = 2 + 3 sin θ

Q: Find an equation (in polar coordinates) of the line tangent to the cycloid x = t - sin t, y = 1 -…

A: Given equations are,

Q: Find the exact length of the polar curve described by: T= 3e-8 on the Interval TSOS 9n.

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Q: A tangent at the pole to the polar curve r = V2 - 2 cos 0 is 0 = A

A: A tangent at the pole to the polar curve r=2-2 cos θ is, for the tangent at the pole we have,…

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Given:

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 5 cos(6) 2

A: To find the length of curve

Q: Find the polar coordinates of the points of intersection of the given curves for O se< 2n. r= sin 8,…

A: To finding intersection points we need to solve the given equation

Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

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Q: aluate the dnd to polar

A: Given that, ∫0a∫02a-x2xx2+y2dxdy Take x=rcosθ, y=rsinθ where 0≤θ≤2π.

Q: The curve (x-)*+Cy +1)*= 4, x 7,1 is given. First draw it in the Cartesian plore and then transtorm…

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Q: 8 sin ( *(4) in the interval 0 < 0< . Calculate the length of the polar curve r =

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Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

Q: Q2 Find the points of intersection of the polar curves r=1+cos and r= -cos

A: Given polar curves are  r=1+cos θ r=-cos θ Find the points of intersection. At first, the value of θ…

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

A: The value of the cosine function  cos0=1cosπ6=32cosπ4=12cosπ3=12cosπ2=0cosπ=-1cos3π=-1cos2π=1

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: 6. Consider the polar curves C1 and C2 described by the polar equations r = 2 – V2 sin(0) and r = 1,…

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Q: 2.Make a sketch of the following polar equation: r = 2 +4 sin 0 (r, 0). Determine also the tangent…

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Q: 4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations…

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Q: 8. Find the equation (in terms of Cartesian variables r and y) of the tangent line to the polar…

A: Given curve is Firstly, we find slope of tangent to polar curve is

Q: A Find a polar equation for 1. (x - 3)2 + (y + 1)2 = 4. 2.x2 + xy + y? = 1

A: Find a polar equation for  ( x -3)2 + (y+1)2 = 4 and x2 + xy + y2 = 1. Here i provide full solution…

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: ulate the length of the polar curve r=1-sin0on the given interval [0,

A: The given curve is r=1-sinθ   ...........(1)  now, differentiate with respect to θ

Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

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Q: Match the graph with its polar equation. r = 2 sin(0) A/2 A/2 4 2 -2 2 4 - 2 2 - 4 A/2 3| л/2 2 1 1…

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