Given the polar equation r = 1+2 cos 0. i. Show that the graph of the equation is symmetrical to the x-axis. ii. Use part (i.) to construct a table for (r, 0) with appropriate values of 0 and sketch the graph of r =1+2 cos 0. (Use the polar grid provided). UT iii. Sketch the graph r = 2 sin 0 on the same diagram as in part (ii.). UTM (2 marks) iv. Find the intersection points between the curves r =1+2 cos 0 and UTM r = 2 sin 0.

Q: A student is asked to determine the polar coordinates (r, 8) corresponding to the Cartesian…

A: Let's find.

Q: 6. What is the equation of the polar curve shown? a) r = -4 sin 30 c) r = 4 cos 30 b) r = 4 sin 30…

A: Since you have asked multiple question so we will be answering only first question. Given polar…

Q: Sketch the curve with the given polar equation.

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Q: Draw phe Polar curve defind by r=4+2 Cos 36

A: Given:

Q: (b) Use appropriate software to sketch the following polar curves i) r = cos(7.10) + cos² (0) ii) =…

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

Q: Graph the polar equation and find the area of the region. Interior of r = 6+3 sin 0 a.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 3. Graph the polar equation and find the area of the region. Outside r = 1 but inside r = 2 sin 20

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Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

A: The given polar equation is  r=5+4cosθ. To find: The slope of the tangent line to the graph of the…

Q: Consider the polar equations r = 9+8 cos(0) and r = 9+8 sin(0), whose graphs are shown below. 15 10-…

A: The graphs of the polar equations r=9+8sinθ and r=9+8 cos θ is given. Identity the given equation…

Q: Find the points at which the polar curve, r = 4 cos θ , has horizontal and vertical tangent lines.

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Q: What is the length of the polar curve below? = 2 cos(0) for 0 sos 4

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Q: 7. Given the polar curve r2 = cos 20, Find the points where the tangent lines are horizontal and…

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Q: 1) Given the Polar Equation r = 2 cos 30 a) Perform the three symmetry test for the equation b)…

A: Symmetry tests: 1. A graph is symmetric with respect to the line θ=π2 (y-axis) if replacing r, θ…

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

A: This is a graph problem

Q: Find the exact length of the polar curve. r = 6 sin ?,    0 ≤ ? ≤ ?/3

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Q: Find the length of the curve over the given interval. polar equation : r = 8a cos θ interval…

A: Given

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

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Q: 3. Graph the polar equation and find the area of the region. Interior ofr= 6+3 sin 0

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Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of e…

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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: 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: Find the exact length of the polar curve r=e2(theta) , where 0 is less than or equal too theta is…

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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: Sketch the curve with the given polar equation, and find its Cartesian equation. 1 1-cos e

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

A: The polar equation is r=2+3sinθ. Recall that fact that x=rcosθ,y=rsinθ. That is,…

Q: Sketch the polar curve with the given equation = -3 cos 0,

A: Polar equation r= -3 cosθ , -π≤θ≤π

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

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Q: Given the polar equation r = 1+2 cos 0. i. Show that the graph of the equation is symmetrical to the…

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

Q: consider the polar equation defined by r = 5 cos(2 sin 8), where s0< 2n. Determine the missing…

A: as points are already find π6,2.70    π3,-0.80    π2,-2.08  3π4,0.77                      π,5…

Q: Consider the polar curve r = sin(30). Sketch the polar curve on the inter 0< 0 < 27/3.

A: Solution: Given data, r = sin(3theta)

Q: 1 Plot the graph of the polar equation r = a 1- cose b Find the corresponding Cartesian equation.“

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Q: Find the length of the polar curve r = −4 sin θ, 0 ≤θ ≤π. Assume that the curve traces out exactly…

A: Find the length of the polar curve r = −4 sin θ, 0 ≤θ ≤π. Assume that the curve traces out exactly…

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

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Q: Which of the following shows the correct sketch of the polar curve r = 9 sin(3 0)? 10 -10 5 10 -5…

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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: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y…

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Q: Which of the following shows the correct sketch of the polar curve r= + 5 cos 0? 4 -6 -4 6 -4 6. b)…

A: r = -(5/2) + 5cos(theta) curve

Q: Which of the following shows the correct sketch of the polar curve r = 6 sin(3 0)? 10 а) -10 10 -10…

A: To plot the polar curve r=6sin3theta

Q: Given the polar equation r = 1+2 cos 0. i. Show that the graph of the equation is symmetrical to the…

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Q: Given the polar equation r =1+2 cos 0. i Show that the graph of the equation is symmetrical to the…

A: He ree e is the solution

Q: Sketch a graph of the polar equation r = 4 cos 30 and find the tangents at the pole. 6. Sketch the…

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Q: Convert the given polar equation into an equation in terms of Cartesian coordinates.

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Q: are polar coor point P, as shown below, find the maximum possible errors in calculating x and y…

A: In this, We find the maximum possible errors in calculating x and y coordinates of the same point.

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: What is the polar equation of the vertical line x = 13? Choose the correct answer below. A. r= 13…

A: Given data is : x=13 What is the polar equation of the vertical line x=13

Q: 10. Sketch the curve of the polar equation r = 2 sin 0 . Find a rectangular equation for this curve.

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Q: Q2. Discuss the symmetry and plot the polar equation r 2-3 sin 0.

A: Given- r=2-3sinθ To find- The symmetry and plot the above polar equation.

Q: Given the polar equation r = 10 sin 9. a. Re-write the equation using rectangular variables, x and…

A: Given : r = 10 sin (θ)

Q: Find the equation of the line tangent to the polar curve at the point r=2cos(theta/3), theta=pi/4

A: Given: The slope of the tangent line is calculated by using the following formula,