QUESTION 8 TM Given the polar equation r= 1+2 cos 0. i. Show that the graph of the equation is symmetrical to the r-axis. UTM 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. UTM iii. Sketch the graph r 2 sin 0 on the same diagram as in part (ii.).

Q: A Moving to another question will save this response. Question 13 Replace the polar equation with an…

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

A: We solve it by following method.

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

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Q: 3. Graph the polar equation r = 3 + 6 sin 0. What type of curve is this?

A: The polar equation r=3+6sinθ

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

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Q: • Question 1. Given the point R (1,4) outside the circle L = x2 + y2 -2y = 1 x² + y2 - 2y - 1 = 0…

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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: Question 22 Find the polar equation for the Cartesian curve ² 0₁ = cos O p = O O sec @tan 0 1 T=…

A: Please see the below picture for detailed solution.

Q: Use a graphing utility to graph the polar equation. Between the loops of r = 5(1 + 2 sin(θ))    How…

A: To find the coordinates we can pick few values for theta, then for those thetas, we can find r.  For…

Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: Question 3 Sketch the polar curve with the given equation "= -5 cos 8, OA. 3 4 OB 3 OC. OD. OE. 1 4

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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: Topic  = Derivatives

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

A: r = 2 r = 4 cosϴ

Q: 3 Convert the equation y = -x to polar form. 3 Then solve the resulting equation for 0. e = 0

A: Explanation of the solution is given below....

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: QUESTION 8 UTM UT i. Show that the graph of the equation is symmetrical to the x-axis. Given the…

A: Graph:

Q: 1. The polar equation of the graph whose equation is x² + y2 = 25 is (A) r- 5cos 0 = 0 (B) r+5cos 0…

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Q: The equation of the polar curve above is E. r = 3 + 2 sin 0 F. r = 3 - 2 sin 0 G. r = 3+ 2 cos 0 H.…

A: From the direction of the cardioid, extending horizontally, that you…

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

A: r =-3cos(theta)

Q: Part A, B, and C

A: According to the given information it is required to sketch the graph of the given polar equation.…

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: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 to z at increments π/6(30°) use a…

A: Given curve r=(1+cosθ)----(1) The objective is to check the symmetry and graph the curve in polar…

Q: Consider the curves: r = 4sin 0 and r = 2 sin(0) + 2cos (8). a) Sketch a graph of both curves on 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: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 4. Sketch a clear and accurate graph of the polar equation r 1-2cos 0.

A: To sketch a clear and accurate graph of the polar equation r=1-2cosθ Here r is the distance from the…

Q: Question 2x² – 2y² = 2x +y 'hich of the following gives the polar form of the equation above? elect…

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

A: We need to sketch the curve with the given polar equation by first sketching the graph of r as a…

Q: 1. Sketch the graph of r = 2 sin(20) in polar coordinate system T/4 31/4 5T/4 7T/4 in the polar…

A: Consider the provided polar equation, Sketch the graph of the polar equation. Now make the graph of…

Q: 6. Consider the polar equation r = 2 – 2 cos(0) a) Complete the table of values for r = 2 -2 cos(0).…

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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: Question 9 Which of the following shows the correct sketch of the polar curve r= -5 cos(3 0) for 0 <…

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Q: a 2 3 4 Identify the coordinates of the point polar form based upon the given conditions. Use pi for…

A: to find the coordinates

Q: Question 19 D The polar curves r 1 cos0 and r 1 t cos0 are shown in the figure above. Which of the…

A: Given two polar curves are r=1+cosθ and r=1-cosθ.

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

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Q: QUESTION 13 dx Given that r cos 0; dy = cos 20. de - sin 20 and de The slope of the tangent line to…

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Q: A particle moves along the polar curve r =1– 2 cos 0 so that = 2. Find the value of d at e = , and…

A: We are given that,                     Now,              When          , Then

Q: 4. Graph the Polar Equation. r = 2 cos 30

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Q: Question 10 Find the rectangular coordinates of the point(s) of intersection of the polar curves r =…

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Q: Q3) sketch the graph of r=cos e in polar coordinates.

A: See the attachment

Q: Which of the following shows the correct sketch of the polar curve r= -5 cos(0)? 61

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Q: Question 3 Transform the polar equation r = 3 cos 0+ sin 0 to an equation in z and y.

A: Let's find.

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: Question 6 Which of the following shows the correct sketch of the polar curve r= - cos(0)? 4 2- a)…

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Q: Which of the following shows the correct sketch of the polar curve r= 4 cos(3 0) for 0 <0<- 10 5 a)…

A: Given:            Polar curve   r=4cos3θ ,  0≤θ≤π2      Using the formula  r=asinnθ or r=acosnθ…

Q: The polar equation r(0) = 4 +5 sin(0) is graphed below. 15+ 14 13 12 11 10 8+ 7 6 + 5 O 4+ 3 2 + +…

A: Above question is solved.