A spiral can be easily graphed using polar coordinates (which you may have learned in pre-calculus), but in regular Cartesian coordinates the formula is a bit more complicated. The standard “Archimedean" spiral has equation y = x tan /x² + y2. dy Find an expression for 2. dx

Q: 7. (-1,–x/6) 8. x2 - y? = 4

A: Given :7. ( -1, -π/6 )8. x2-y2=4

Q: The curve whose equation in polar coordinates is given by r -4 sin(@) is a circle with its center…

A: I am going to solve the given problem first by converting in to the cartesian form and then…

Q: Graph polar equation r = 2 sin 3θ. Be sure to test for symmetry.

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Q: 1) Find the exact length of the polar curve r = 2+2 cos 0. Show All Your Work!

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Q: Which of the following shows the correct sketch of the polar curve r= -10+ 10 sin(0)?

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Q: Find the circumference of a circle described by the parametric equations = 7 cos 0 and y = 7sin 0…

A: The formula L=∫dxdθ2+dydθ2dθ is formula for length of arc in polar coordinates. As we go along the…

Q: r2 = sin 20 - 3cos0

A: We need to plot the graph of r2=sin2θ-3cosθ. Any point on the polar coordinate system can be…

Q: The graph of the curve given by the parametric equations X=sint and y=cos2t IS à Select one: O ircle…

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Q: Determine the points at which the limacon defined by the polar equation r= 3 + 2 sin 0 Has…

A: Given r=3+2sinθ

Q: a) A curve has the parametric equation given as x = 4+3 cos 0 y = 3 sin 0 – 2. i) Convert the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find a polar equation for the curve represented by the given Cartesian equatic y = 4

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

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Q: Sketch the graph of the curve with the polar equation: r=2– sin(20).

A: To draw a polar graph we need to check its symmetricity by using following   #  In the first test,…

Q: Below you are given six polar equations and plots of four of these curves. Match each plot with the…

A: Consider the curves

Q: Test for symmetry and then graph polar equation r = 2 + 2 cos θ.

A: Given polar equation is r=2+2cosθ. (i) Check for symmetry about the line θ=π2. Replace r,θ with…

Q: Graph the polar equations r = −1+cos θ and find the equation of the tangent at θ = π/4.

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Q: Find a Cartesian equation for the curve represented by polar equation . r = 14 cos 0- 12 sin 0.

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Q: Sketch a graph of the polar equation r = 3 sin 2 and find the tangent line(s) at the pole (if any).

A: We have to sketch a graph of the polar equation r=3sin2θand then we have to find the tangent line(s)…

Q: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…

Q: A bumblebee is flying so that its position is given by~r(t) = cos(2t), cos(3t),sin(5t) for the…

A: Before we start the problem let us get to know the formula first.

Q: For this problem sketch the curve with the given polar equation for parts a) and b) a) r = - 3…

A: r =-3cos(theta)

Q: 01: If x²+y-2x=0. Find the corresponding equation in polar. Sketch.

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Q: Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in…

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Q: Use to graph the polar equations given below for 0 < 0 < 2ñ. Which one does NOT have a graph with 4…

A: Not have a graph of four petals is

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

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Q: A curve with polar equation r = 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian…

A: The polar equation is, r=58sinθ+49cosθ   Rewrite the equation. 8rsinθ+49rcosθ=5   Substitute y for…

Q: Sketch the curve r-4 sin 30 with the given polar equation by: first sketching the graph of as a…

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Q: Find a Cartesian equation whose graph is the same as that of the polar equa- 1² cos 20 and (hence or…

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Q: What type of limacon is the graph of the polar equation given by r = √3+ cos 0? O Limacon with a…

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Q: Find the equation of the tangent line to the polar curve r = 2 – sin(θ) at θ = π/3. Draw

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Q: 5 cos 0 and use this Cartesian equation to 5. Find a Cartesian equation for the polar curve r =…

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Q: r 1 1 sing at Ø 元-6

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Q: Find the smallest interval for θ starting with θ min = 0 so that your graphing utility graphs the…

A: Consider the given polar equation, r=4sin2θ use the Desmos graphing calculator to graph the…

Q: The area of one loop of the graph of the polar equation r= 2 sin 30 is Select one:

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Q: Find the lengths of the curves given by the polar coordinate equations r = 2 sin θ + 2 cos θ, 0 ≤ θ…

A: Given: r=2sinθ+2cosθ; 0≤θ≤π2 for finding length of curve given by the given polar equation, first we…

Q: The area of one loop of the graph of the polar equation r = 2 sin 30 is Select one: IT 3 2 4 2n 3

A: Solve by definite integration

Q: 8. First graph the polar curve r= sin(20) on 0<60<2n and plot the point on the curve that…

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Q: Of a circle of radius "a" whose center is point (1,-1).Write the equation in Polar Coordinates.…

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Q: Which of the following shows the correct sketch of the polar curve r = -8 + 8 sin(0)?

A: The given polar equation is: r=-8+8sin(θ)

Q: Which of the following is the closest distance from the points on the curve given by the equation r…

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Q: The curve given by the polar equation r = a(1– cos ) is called a The cardioid has equation (22 + y?…

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Q: On the left side, the polar function 1 = 2 cos(0)+3 sin(0) is graphed. Enter a possible rectangular…

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Q: Which of the following shows the correct sketch of the polar curve r = 9 – 9 cos(0)?

A: We have to do following steps to solve it.

Q: Determine the points at which the limacon defined by the polar equation r= 3 +2 sin e Has horizontal…

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Q: . The graph of the parametric curve x = cos^3θ, y = sin^3θ for 0 ≤θ ≤2π is a closed astroid of four…

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Q: TRUE OR FALSE. The curve defined by the polar equation r = 2 + 3 sin θ is symmetric with respect to…

A: To determine whether the given statement is true or false.